8th Gradecontent.njctl.org › courses › math › 8th-grade-math › 3d...2015/11/20 · Slide 1 / 97 8th Grade 3D Geometry 2015-11-20 Slide 2 / 97 Table of Contents · Prisms and

Slide 1 / 97

8th Grade

3D Geometry

2015-11-20

www.njctl.org

Slide 2 / 97

Table of Contents

· Prisms and CylindersVolume

· Pyramids, Cones & Spheres

Click on the topic to go to that section

More Practice/ Review

3-Dimensional Solids

Glossary & Standards

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http://www.njctl.org

http://www.njctl.org

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Table of Contents

· Prisms and CylindersVolume

· Pyramids, Cones & Spheres

Click on the topic to go to that section

More Practice/ Review


Glossary & Standards[This object is a pull tab]

Teac

her N

otes Vocabulary Words are bolded

in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it.

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Return toTable ofContents

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The following link will take you to a site with interactive 3-D figures and nets.

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http://www.learner.org/interactives/geometry/3d_prisms.html

Polyhedron A 3-D figure whose faces are all polygons.

Polyhedron Not Polyhedron

Sort the figures into the appropriate side.

Polyhedron

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3-Dimensional SolidsCategories & Characteristics of 3-D Solids:

Prisms1. Have 2 congruent, polygon bases which are parallel to one another2. Sides are rectangular (parallelograms)3. Named by the shape of their base

Pyramids1. Have 1 polygon base with a vertex opposite it2. Sides are triangular3. Named by the shape of their base

click to reveal

click to reveal

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3-Dimensional SolidsCategories & Characteristics of 3-D Solids:

Cylinders1. Have 2 congruent, circular bases which are parallel to one another2. Sides are curved

Cones1. Have 1 circular bases with a vertex opposite it2. Sides are curvedclick to reveal

click to reveal

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Edge Line segment formed where 2 faces meet

Vertex (Vertices) Point where 3 or more faces/edges meet

3-Dimensional SolidsVocabulary Words for 3-D Solids:

Polyhedron A 3-D figure whose faces are all polygons (Prisms & Pyramids)

Face Flat surface of a Polyhedron

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Sort the figures.If you are incorrect, the figure will be sent back.

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1 Name the figure.

A Rectangular Prism B Triangular Pyramid C Hexagonal Prism D Rectangular PyramidE Cylinder F Cone

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1 Name the figure.

A Rectangular Prism B Triangular Pyramid C Hexagonal Prism D Rectangular PyramidE Cylinder F Cone

[This object is a pull tab]

Ans

wer

D


2 Name the figure.

A Rectangular Pyramid B Triangular Prism C Octagonal Prism D Circular Pyramid E Cylinder F Cone

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2 Name the figure.

A Rectangular Pyramid B Triangular Prism C Octagonal Prism D Circular Pyramid E Cylinder F Cone


Ans

wer

E


3 Name the figure.

A Rectangular Pyramid B Triangular Pyramid C Triangular Prism D Hexagonal Pyramid E Cylinder F Cone

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3 Name the figure.

A Rectangular Pyramid B Triangular Pyramid C Triangular Prism D Hexagonal Pyramid E Cylinder F Cone


Ans

wer

B


4 Name the figure.

A Rectangular Prism B Triangular Prism C Square Prism D Rectangular Pyramid E Cylinder F Cone

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4 Name the figure.

A Rectangular Prism B Triangular Prism C Square Prism D Rectangular Pyramid E Cylinder F Cone


Ans

wer

A


5 Name the figure.

A Rectangular Prism B Triangular Pyramid C Circular Prism D Circular Pyramid E Cylinder F Cone

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5 Name the figure.

A Rectangular Prism B Triangular Pyramid C Circular Prism D Circular Pyramid E Cylinder F Cone


Ans

wer

F


For each figure, find the number of faces, vertices and edges.Can you figure out a relationship between the number of faces, vertices and edges of 3-Dimensional Figures?

Name Faces Vertices Edges

Cube 6 8 12

Rectangular Prism 6 8 12

Triangular Prism 5 6 9

Triangular Pyramid 4 4 6

Square Pyramid 5 5 8

Pentagonal Pyramid 6 6 10

Octagonal Prism 10 16 24

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Euler's Formula

F + V = E + 2

Euler's Formula is the number of edges plus 2 is equal to the sum of the faces and vertices.

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6 How many faces does a pentagonal prism have?

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6 How many faces does a pentagonal prism have?


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7


7 How many edges does a rectangular pyramid have?

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7 How many edges does a rectangular pyramid have?


Ans

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8


8 How many vertices does a triangular prism have?

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8 How many vertices does a triangular prism have?


Ans

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6


9 How many faces does a hexagonal pyramid have?

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9 How many faces does a hexagonal pyramid have?


Ans

wer

7


10 How many vertices does a triangular pyramid have?

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10 How many vertices does a triangular pyramid have?


Ans

wer

4


Volume


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Label

- Units3 or cubic units

Volume

Volume

- The amount of space occupied by a 3-D Figure - The number of cubic units needed to FILL a 3-D Figure (layering)click to reveal

click to reveal

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Label

- Units3 or cubic units

Volume

Volume

- The amount of space occupied by a 3-D Figure - The number of cubic units needed to FILL a 3-D Figure (layering)click to reveal

click to reveal


Mat

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e MP.6: Attend to Precision.

Ask: What labels (or units) should we use with our answers?


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Volume Activity

Click the link below for the activity.

Lab #1: Volume Activity

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Volume Activity

Click the link below for the activity.

Lab #1: Volume Activity


Teac

her N

otes The URL for the lab is:

http://njctl.org/courses/math/8th-grade-math/3d-geometry/volume-activity/


Volume of Prisms & Cylinders


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http://www.njctl.org/courses/math/8th-grade-math/3d-geometry/volume-activity/



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Volume

Volume of Prisms & Cylinders:

Area of Base x Height, or V = Bh

Area Formulas:

Rectangle = lw or bh

Triangle = bh or 2 Circle = πr2

click to reveal

(bh) 1 2

click to reveal

click to reveal

click to reveal

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Find the Volume

5 m

8 m

2 m

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Find the Volume

5 m

8 m

2 m


Ans

wer

VOLUME: 2x 5 10 (Area of Base)x 8 (Height)80 m3

VOLUME:V = B hV = l w hV = 5 2 8V = 10 8V = 80 m3


Find the Volume Use 3.14 as your value of π.

10 yd

9 yd

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Find the Volume Use 3.14 as your value of π.

10 yd

9 yd


Ans

wer

VOLUME: 9 x 9 81x 3.14 254.34 x 10 2543.4 yd3

VOLUME:V = B hV = r2 hV = 3.14 92 10V = 3.14 81 10V = 254.34 10V = 2543.4 yd3

(Are

a of B

ase)

(Height)


A cylinder with a radius measuring 2 cm and a height of 5 cm is compared to a cylinder with a radius of 4 cm and a height of 5 cm. Amy says that the volume of the cylinder with a radius of 4 cm is double the volume of the cylinder with a radius of 2 cm. She used 3.14 as her value of π. Is she correct? Explain your reasoning.

Start by calculating the volume of both cylinders.

V = (3.14)(2)2(5)

V = 62.8 cm3

V = (3.14)(4)2(5)

V = 251.2 cm3

Answer the question.

No, Amy is not correct. If the radius of the cylinder doubles, the volume does not double. Instead it quadruples.

click click

click

Find the Volume

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A cylinder with a radius measuring 2 cm and a height of 5 cm is compared to a cylinder with a radius of 4 cm and a height of 5 cm. Amy says that the volume of the cylinder with a radius of 4 cm is double the volume of the cylinder with a radius of 2 cm. She used 3.14 as her value of π. Is she correct? Explain your reasoning.

Start by calculating the volume of both cylinders.

V = (3.14)(2)2(5)

V = 62.8 cm3

V = (3.14)(4)2(5)

V = 251.2 cm3

Answer the question.

No, Amy is not correct. If the radius of the cylinder doubles, the volume does not double. Instead it quadruples.

click click

click

Find the Volume


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e

MP.3 - Construct viable arguments & critique the reasoning of others.

After calculating the volume of both cylinders, ask:

What do you think about what Amy predicted?

Do you agree? Why or Why not?


Teachers:

Use this Mathematical Practice Pull Tab for the next 9 SMART Response slides.

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Teachers:

Use this Mathematical Practice Pull Tab for the next 9 SMART Response slides.


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MP.5 - Use appropriate tools strategically.

Ask: Can you make a model to show that?

Would it help to create a diagram/draw a picture?


4 in

11 Find the Volume.

7 in 1 5

1 in 1 2

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4 in

11 Find the Volume.

7 in 1 5

1 in 1 2


Ans

wer

VOLUME: 7.2 x 1.5 10.8 (Area of Base)x 4 (Height) 43.2 in3

VOLUME:V = B hV = 7.2(1.5)(4)V = 43.2 in3


12 Find the volume of a rectangular prism with length 2 cm, width 3.3 cm and height 5.1 cm.

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12 Find the volume of a rectangular prism with length 2 cm, width 3.3 cm and height 5.1 cm.


Ans

wer

VOLUME:V = B hV =2(3.3)(5.1)V = (6.6)(5.1)V = 33.66 cm3


13 Which is a possible length, width and height for a rectangular prism whose volume = 18 cm 3

A 1 x 2 x 18B 6 x 3 x 3C 2 x 3 x 3D 3 x 3 x 3

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13 Which is a possible length, width and height for a rectangular prism whose volume = 18 cm 3

A 1 x 2 x 18B 6 x 3 x 3C 2 x 3 x 3D 3 x 3 x 3


Ans

wer

C


14 Find the volume.

21 ft

42 ft

50 ft47 ft

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14 Find the volume.

21 ft

42 ft

50 ft47 ft


Ans

wer

V = Bh & B = bh of the triangle

V = (21)(42)(50)

V = (882)(50)

V = 441(50)V = 22,050 ft3

1 2

1 2 1 2


15 A box-shaped refrigerator measures 12 by 10 by 7 on the outside. All six sides of the refrigerator are 1 unit thick. What is the inside volume of the refrigerator in cubic units?

HINT: You may want to draw a picture!

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15 A box-shaped refrigerator measures 12 by 10 by 7 on the outside. All six sides of the refrigerator are 1 unit thick. What is the inside volume of the refrigerator in cubic units?

HINT: You may want to draw a picture!


Ans

wer

10 in.7 in.

12 in.

8 in. 5 in.

10 in.


16 Find the volume. Use 3.14 as your value of π.

6 m

10 m

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6 m

10 m


Ans

wer

d = 10 m, so r = 5 m

V = r2 hV = 3.14 52 6V = 3.14 25 6V = 78.5 6V = 471 m3


17 Which circular glass holds more water?

Note: Use 3.14 as your value of π.

AGlass A having a 7.5 cm diameter and standing 12 cm high

BGlass B having a 4 cm radius and a height of 11.5 cm

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17 Which circular glass holds more water?

Note: Use 3.14 as your value of π.

AGlass A having a 7.5 cm diameter and standing 12 cm high

BGlass B having a 4 cm radius and a height of 11.5 cm


Ans

wer

Glass Ad = 7.5, so r = 3.75V = B hV = r2 hV = 3.14 (3.75)2 12V = 3.14 14.0625 12V = 529.875 cm3 Glass B

V = B hV = r2 hV = 3.14 (4)2 11.5V = 3.14 16 11.5V = 577.76 cm3


18 What is the volume of the largest cylinder that can be placed into a cube that measures 10 feet on an edge? Use 3.14 as your value of π.

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18 What is the volume of the largest cylinder that can be placed into a cube that measures 10 feet on an edge? Use 3.14 as your value of π.


Ans

wer d = 10 ft, so r = 5 ft & h = 10 ft

V = π (52)(10)V = π(25)(10)V = 785 ft3


19 A circular garden has a diameter of 20 feet andis surrounded by a concrete border that has a width of three feet and a depth of 6 inches. What is the volume of concrete in the path? Use 3.14 as your value of π.

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19 A circular garden has a diameter of 20 feet andis surrounded by a concrete border that has a width of three feet and a depth of 6 inches. What is the volume of concrete in the path? Use 3.14 as your value of π.


Ans

wer

dinner = 20, so rinner = 10 ftrouter = 10 + 3 = 13 ftV = Bh = πr2hV = [π(132) - π(102)](0.5)V = (169π - 100π)(0.5)V = (216.66)(0.5)V = 108.33 ft3


Sometimes, a question will ask you to "Leave your answer in terms of π". This means that you treat π like a variable & only do the arithmetic operations with the remaining numbers.

Ex: If a cylinder has a radius of 3 and a height of 4, then

Volume = π(3)2(4)

= π(9)(4)

= 36π units2

Let's try some more problems like this one.

Click here to return to cones & spheres.

Answer in Terms of π

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Leave your answer in terms of π.

10 yd

9 yd

Find the Volume

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10 yd

9 yd

Find the Volume


Ans

wer

VOLUME:V = B hV = r2 hV = 92 10V = 81 10V = 810 yd3


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30 ft

15 ft


Find the Volume

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30 ft

15 ft


Find the Volume


Ans

wer

d = 15, so r = 7.5VOLUME:V = B hV = r2 hV = (7.5)2 30V = 56.25 30V = 1687.5 ft3


20 A cylinder has a radius of 7 and a height of 2. What is its volume? Leave your answer in terms of π.

A 14π units3

B 28π units3

C 49π units3

D 98π units3

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20 A cylinder has a radius of 7 and a height of 2. What is its volume? Leave your answer in terms of π.

A 14π units3

B 28π units3

C 49π units3

D 98π units3 [This object is a pull tab]

Ans

wer

V = BhV = (7)2 2V = 49 2V = 98 units3

ππ

π

D


21 A cylinder has a diameter of 12 in. and a height of 12 in. What is its volume? Leave your answer in terms of π.

A 144π in3

B 432π in3

C 864π in3

D 1,728π in3

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A 144π in3

B 432π in3

C 864π in3

D 1,728π in3 [This object is a pull tab]

Ans

wer

d = 12 in., so r = 6 in.V = BhV = (6)2 12V = 36 12V = 432 in3

ππ

πB



A 106.25π in3

B 361.25π in3

C 425π in3

D 1,228.25π in3

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A 106.25π in3

B 361.25π in3

C 425π in3

D 1,228.25π in3 [This object is a pull tab]

Ans

wer

d = 17 in., so r = 8.5 in.V = BhV = (8.5)2 5V = 72.25 5V = 361.25 in3

ππ

πB


23 A circular pool has a diameter of 40 feet and is surrounded by a wooden deck that has a width of 4 feet and a depth of 6 inches. What is the volume of the wooden deck? Leave your answer in terms of π.

A 88π ft3

B 176π ft3

C 400π ft3

D 576π ft3

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23 A circular pool has a diameter of 40 feet and is surrounded by a wooden deck that has a width of 4 feet and a depth of 6 inches. What is the volume of the wooden deck? Leave your answer in terms of π.

A 88π ft3

B 176π ft3

C 400π ft3

D 576π ft3 [This object is a pull tab]

Ans

wer

pool: d = 40 ft, so r = 20 ftdeck: r = 20 + 4 = 24 ftV = ( (24)2 - (20)2)(0.5)V = (576 - 400 )0.5V = 176 (0.5) V = 88 ft3

ππ

π

ππ

π

A


Volume of Pyramids, Cones & Spheres


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Demonstration comparing volume of Cones & Spheres with volume of

Cylinders

click to go to web site

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(Area of Base x Height) = Bh 1 3

1 3

A cone is 1/3 the volume of a cylinder with the same base area (B) and height (h).

Area of Base x Height3

Bh3=

Volume of a Cone

click to reveal

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http://www.learner.org/courses/learningmath/measurement/session8/part_b/cylinders.html

V = 2/3 (Volume of Cylinder)

r2 h( )2/3 V=or

V = 4/3 r3ππ

Volume of a Sphere

A sphere is 2/3 the volume of a cylinder with the same base area (B) and height (h).

click to reveal

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V = 2/3 (Volume of Cylinder)

r2 h( )2/3 V=or

V = 4/3 r3ππ

Volume of a Sphere

A sphere is 2/3 the volume of a cylinder with the same base area (B) and height (h).

click to reveal


Figu

re


How much ice cream can a Friendly’s Waffle cone hold if it has a diameter of 6 in and its height is 10 in? Use 3.14 as your value of π.

(Just Ice Cream within Cone. Not on Top)Volume and Mass used in portion control. $$$

Volume

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How much ice cream can a Friendly’s Waffle cone hold if it has a diameter of 6 in and its height is 10 in? Use 3.14 as your value of π.

(Just Ice Cream within Cone. Not on Top)Volume and Mass used in portion control. $$$

Volume


Ans

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&

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V = (3.14)(32)(10)

V = 92.3 in3

1 3

Questions to address MP.1:What information are you given? What is this problem asking?

Questions to address MP.4:Write a number sentence to model this problem.What connections do you see?



4 in

9 in

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4 in

9 in


Ans

wer

V = Bh

V = (π42)(9)

V = (16π)(9)

V = 3(50.24)V = 150.72 in3

1 3 1 3 1 3


25 Find the Volume. Use 3.14 as your value of π.

5 cm8 cm

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5 cm8 cm


Ans

wer

V = Bh

V = (π52)(8)

V = (25π)(8)

V = (200π)

V = 209 cm3

1 3 1 3 1 3 1 3

1 3


V = πr3

V = (3.14)(5.5)3

V = 696.6 cm3

4 3 4 3

If the radius of a sphere is 5.5 cm, what is its volume? Use 3.14 as your value of π.

Click here

Volume

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26 What is the volume of a sphere with a radius of 8 ft? Use 3.14 as your value of π.

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26 What is the volume of a sphere with a radius of 8 ft? Use 3.14 as your value of π.


Ans

wer V = πr3

V = (3.14)(8)3

V = 2,143.57 ft3

4 3 4 3


27 What is the volume of a sphere with a diameter of 4.25 in? Use 3.14 as your value of π.

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27 What is the volume of a sphere with a diameter of 4.25 in? Use 3.14 as your value of π.


Ans

wer

d = 4.25, so r = 2.125

V = πr3

V = (3.14)(2.125)3

V = 40.17 in3

4 3 4 3


Similar to when we found the volume of a cylinder, with a cone and a sphere, you could be asked to "Leave your answer in terms of π".

Click here if you need to review that property.

Volume in Terms of π

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You are selling lemonade in conic cups (cups shaped like cones). How much lemonade will each customer get to drink? Leave your answer in terms of π.

8 cm

11 cm


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You are selling lemonade in conic cups (cups shaped like cones). How much lemonade will each customer get to drink? Leave your answer in terms of π.

8 cm

11 cm



Ans

wer

d = 8 cm, so r = 4 cm

V = (4)2 (11)

V = (16)(11)

V = cm3 = 58.6 cm3

1 3 1 3

π

π

π176 3

π


If the radius of a sphere is 6 cm, what is its volume? Leave your answer in terms of π.


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If the radius of a sphere is 6 cm, what is its volume? Leave your answer in terms of π.



Ans

wer

V = (6)3

V = (216)

V = cm3

V = 288 cm3

4 3 4 3

π

π

π864 3

π


28 Find the volume of the cone below. Leave your answer in terms of π.

A 12π in3

B 36π in3

C 48π in3

D 144π in3 4 in

9 in

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A 12π in3

B 36π in3

C 48π in3

D 144π in3 4 in

9 in


Ans

wer

V = (4)2 (9)

V = (16)(9)

V = (16)(3)V = 48 in3

1 3 1 3

π

π

ππ

C


29 Find the volume of the sphere that has a diameter of 18 cm. Leave your answer in terms of π.

A 729π cm3

B 972π cm3

C 5,832π cm3

D 7,776π cm3

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29 Find the volume of the sphere that has a diameter of 18 cm. Leave your answer in terms of π.

A 729π cm3

B 972π cm3

C 5,832π cm3

D 7,776π cm3


Ans

wer

d = 18 cm, so r = 9 cm

V = (9)3

V = (729)

V =

V = 972 cm3

4 3 4 3

π

π

π

π2916 3

B



A 49π in3

B 84π in3

C 147π in3

D 252π in3 7 in

12 in

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A 49π in3

B 84π in3

C 147π in3

D 252π in3 7 in

12 in


Ans

wer

d = 7 in., so r = 3.5 in.

V = (3.5)2 (12)

V = (12.25)(12)

V = (12.25)(4)V = 49 in3

1 3 1 3

π

π

ππ

A


31 Find the volume of a sphere that has a radius of 4.5 cm. Leave your answer in terms of π.

A 27π cm3

B 91.125π cm3

C 121.5π cm3

D 364.5π cm3

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31 Find the volume of a sphere that has a radius of 4.5 cm. Leave your answer in terms of π.

A 27π cm3

B 91.125π cm3

C 121.5π cm3

D 364.5π cm3 [This object is a pull tab]

Ans

wer

V = (4.5)3

V = (91.125)

V =

V = 121.5 cm3

4 3 4 3

π

π

π

π364.5 3

C


32 A sphere with a radius measuring 9 cm is compared to a sphere with a radius of 18 cm. Jeff says that the volume of the sphere with a radius of 18 cm is double the volume of the sphere with a radius of 9 cm. Is he correct? Explain your reasoning. When you are done calculating your answer, type in the number "1".

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32 A sphere with a radius measuring 9 cm is compared to a sphere with a radius of 18 cm. Jeff says that the volume of the sphere with a radius of 18 cm is double the volume of the sphere with a radius of 9 cm. Is he correct? Explain your reasoning. When you are done calculating your answer, type in the number "1".


Ans

wer

V = (9)3

V = (729)

V =

V = 972 cm3

4 3 4 3

π

π

π

π2,916 3

V = (18)3

V = (5,832)

V =

V = 7,776 cm3

4 3 4 3

π

π

π

π23,328 3

7,776 is not double the volume of 972 . It's 8 times bigger.

ππ


(Area of Base x Height) = Bh 1 3

1 3

Area of Base x Height3

Bh3=

Volume of a Pyramid

A pyramid is 1/3 the volume of a prism with the same base area (B) and height (h).

click to reveal

Slide 67 / 97

Pyramids are named by the shape of their base..

The volume is a pyramid is 1/3 the volume of a prism with the same base area(B) and height (h).

V = Bh13

=5 m

side length = 4 m

V = Bh

V = (4)(4)(5)

V = (80)

V = 26 m3

1 3 1 3 1 3

2 3

Click here

Pyramids

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33 Find the Volume of a triangular pyramid with a base edge of 8 in, base height of 4 in and a pyramid height of 10 in.

8 in

10 in

4 in

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33 Find the Volume of a triangular pyramid with a base edge of 8 in, base height of 4 in and a pyramid height of 10 in.

8 in

10 in

4 in


Ans

wer

V = Bh

V = [ (4)(8)](10)

V = [ (32)](10)

V = (16)(10)

V = 53 in3

1 3 1 3 1 3

1 3

1 3

1 2 1 2


34 Find the volume.

8 cm

7 cm

15.3 cm

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34 Find the volume.

8 cm

7 cm

15.3 cm


Ans

wer

V = Bh

V = (8)(7)(15.3)

V = (56)(15.3)

V = 285.6 cm3

1 3 1 3 1 3


More Practice / Review


Slide 71 / 97

35 Find the volume.

15 mm

8 mm

22 mm

Slide 72 / 97

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35 Find the volume.

15 mm

8 mm

22 mm


Ans

wer

V = Bh

V = (15)(8)(22)

V = 880 mm3

1 3 1 3


36 Find the volume of a rectangular pyramid with a base length of 2.7 meters and a base width of 1.3 meters, and the height of the pyramid is 2.4 meters.

HINT: Drawing a diagram will help!

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36 Find the volume of a rectangular pyramid with a base length of 2.7 meters and a base width of 1.3 meters, and the height of the pyramid is 2.4 meters.

HINT: Drawing a diagram will help!


Ans

wer

V = Bh

V = (2.7)(1.3)(2.4)

V = 2.808 m3

1 3 1 3


37 Find the volume of a square pyramid with base edge of 4 inches and pyramid height of 3 inches.

Slide 74 / 97

37 Find the volume of a square pyramid with base edge of 4 inches and pyramid height of 3 inches.


Ans

wer

V = Bh

V = (42)(3)

V = 16 in3

1 3 1 3


38 Find the Volume.

9 m9 m

12 m

11 m

6 m

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38 Find the Volume.

9 m9 m

12 m

11 m

6 m[This object is a pull tab]

Ans

wer

V = Bh

V = [ (9)(6)](11)

V = (27)(11)

V = 99 m3

1 3 1 3

1 2

1 3



14 ft

21 ft

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14 ft

21 ft


Ans

wer

V = Bh

V = π(72)(21)

V = (3.14)(49)(21)

V = 1,077.02 ft3

1 3 1 3 1 3



8 in

6.9 in

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8 in

6.9 in


Ans

wer

V = Bh

V = π(42)(6.9)

V = (3.14)(16)(6.9)

V = 115.552 in3

1 3 1 3 1 3


41 Find the Volume.

4 ft

7 ft

8 ft

9 ft

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41 Find the Volume.

4 ft

7 ft

8 ft

9 ft


Ans

wer V = Bh

V = 7(4) (8) 2V= 112 ft3


42 A cone 20 cm in diameter and 14 cm high was used to fill a cubical planter, 25 cm per edge, with soil. How many full cones of soil were needed to fill the planter?

20 cm

14 cm

25 cm

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42 A cone 20 cm in diameter and 14 cm high was used to fill a cubical planter, 25 cm per edge, with soil. How many full cones of soil were needed to fill the planter?

20 cm

14 cm

25 cm[This object is a pull tab]

Ans

wer

Cone Cube1/3(3.14)(102)(14) 253

1465.3 cm3 15625 cm3

15625/1465.3 # 10.7 about 11 cones


43 Find the Volume.

7 in8 in

9 in

9 in

2 in

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43 Find the Volume.

7 in8 in

9 in

9 in

2 in


Ans

wer

V = BhV = 7(2) (8) 2V= 56 in3


Name a 3-D Figure that is not a polyhedron.

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Name a 3-D Figure that is not a polyhedron.


Ans

wer possible answers

cylindercone


Name a 3-D figure that has 6 rectangular faces.

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Name a 3-D figure that has 6 rectangular faces.


Ans

wer

rectangular prism


44 Find the volume.

40 m

70 m

80 m

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44 Find the volume.

40 m

70 m

80 m


Ans

wer V = Bh

V = 80(40)(70)V = 224,000 m3


45 The figure shows a right circular cylinder and a right circular cone. The cylinder and the cone have the same base and the same height.

Part A: What is the volume of the cone, in cubic feet?

From PARCC EOY sample test calculator #11

A 12π ft3

B 16π ft3

C 36π ft3

D 48π ft3

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http://practice.parcc.testnav.com/#

45 The figure shows a right circular cylinder and a right circular cone. The cylinder and the cone have the same base and the same height.

Part A: What is the volume of the cone, in cubic feet?

From PARCC EOY sample test calculator #11

A 12π ft3

B 16π ft3

C 36π ft3

D 48π ft3


Ans

wer

V = (4)2 (3)

V = (16)(3)

V = (16)V = 16 ft3

1 3 1 3

π

π

ππ

B


46 Part B: What is the ratio of the cone's volume to the cylinder's volume?

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46 Part B: What is the ratio of the cone's volume to the cylinder's volume?


Ans

wer

Cylinder: V = (4)2(3)V = (16)(3)V = 48 ft3

ππ

ππ

Cone:V = 16 ft3

Ratio = = 16π48π

1 3


http://practice.parcc.testnav.com/#



Slide 86 / 97




Teac

her N

otes Vocabulary Words are bolded

in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it.


tip

traffic cone

cone

pencil

ice cream

Back to

Instruction

curved

polyhedron

surface

Cone A polyhedron that has one circular base with a vertex opposite of it

and sides that are curved.

Slide 87 / 97

page0svg

page0svg

page5svg

candles

pizza

Pringles

can

Back to

Instruction

curved

polyhedron

surface

Cylinder A polyhedron that has two congruent

circular bases which are parallel to one another and sides that are curved.

Slide 88 / 97

Back to

Instruction

Edge

Line segment formed where 2 faces meet.

A triangular pyramid has 6

edges.

Slide 89 / 97

Back to

Instruction

Euler's Formula

The number of edges plus 2 is equal to the sum of the faces and vertices.

E + 2 = F + V

E + 2= F + VE + 2 = 4 + 4

E + 2 = 8E = 6faces = 4

vertices = 4pyramid:

Slide 90 / 97

page5svg

page6svg

page8svg

Back to

Instruction

Face

Flat surface of a polyhedron.

A triangular pyramid has 4 faces. (there is

one you can't see)

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Back to

Instruction

Polyhedron

A 3-D figure whosefaces are all polygons.

Cubes

Prisms

Pyramids

Made of:

Faces

Edges

Vertices

Cylinders

Cones

Slide 92 / 97

Rectangular

PrismTriangular

Prism

Prism

Pentagonal

Back to

Instruction

Prism A polyhedron that has two congruent,

polygon bases which are parallel to one another, sides that are rectangular,

and named by the shape of their base.

Block of cheese

bodyof

pencil

juicebox

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Pentagonal Pyramid

SquarePyramidTriangular

Pyramid

Back to

Instruction

Pyramid

A polyhedron that has one polygon base with a vertex opposite of it,sides that are triangular,

and named by the shape of its base.

Slide 94 / 97

Back to

Instruction

Vertex

Point where two or more straight lines/faces/edges meet.

A Corner.

A triangular pyramid has 4

vertices.

Slide 95 / 97

Back to

Instruction

Volume

The number of cubic units needed to fill a 3D figure (layering).

The amount of space occupied by a 3D figure.

Label: Units3

or cubic units

volume of prisms

and cylinders:

area of base x height

V = area of base x h V = 2m x 5m x 8m

V = 80m3

Slide 96 / 97

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Standards for Mathematical Practices

Click on each standard to bring you to an example of how to meet

this standard within the unit.

MP8 Look for and express regularity in repeated reasoning.

MP1 Make sense of problems and persevere in solving them.

MP2 Reason abstractly and quantitatively.

MP3 Construct viable arguments and critique the reasoning of others.

MP4 Model with mathematics.

MP5 Use appropriate tools strategically.

MP6 Attend to precision.

MP7 Look for and make use of structure.

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http://www.corestandards.org/Math/Practice/#CCSS.Math.Practice.MP1

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Documents

8th Gradecontent.njctl.org › courses › math › 8th-grade-math › 3d...2015/11/20 · Slide 1 / 97 8th Grade 3D Geometry 2015-11-20 Slide 2 / 97 Table of Contents · Prisms and