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Page 1 CCM6 UNIT 12 SA and V
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UNIT 12
Volume and Surface Area
CCM6
Name: ________________
Math Teacher:___________
Projected Test Date:_____
Unit 12 Table of Contents Unit 12 Vocabulary…………………………………..……………………………..…….......….….2
Days 1: Basics of 3-D Figures……………………………………….…………………………3-7
Day 2: Surface Area Of Rectangular Prisms…………..………………………………...…8-10
Day 3: Surface Area and NETS……………………………………………………………...11-12
Day 4: Surface Area of Compound 3-D Shapes………………………………………….13-16
Day 5: Volume of Prisms………………………………………………………………..…....17-18
Day 6: Problem Solving with Volume…………………..………………………….……….19-21
Day 7: Volume of Rectangular Prisms with Fractional Edges……..………......……...22-24
Unit Review/Study Guide……………………………………………………………...………25-27
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Unit 12 Vocabulary
polyhedron three-dimensional figure whose surfaces, or faces, are all polygons
area the amount of square units covered by a plane figure measured in square units
net an arrangement of two-dimensional figures that can be folded to form a polyhedron (3-D figure)
surface area the sum of the area of the faces of a 3D figure
face a flat surface of a polyhedron (a 3D figure)
edge the line segment along which two faces of a polyhedron intersect
vertices a point where three or more edges intersect
pyramid a polyhedron that has a polygon base and triangular lateral faces
right prism a polyhedron that has two parallel congruent polygon bases. All lateral faces are rectangles.
rectangular prism 3d figure where 6 faces are rectangles
volume the number of cubic units needed to fill a given space
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Day 1: 3-D Figures Big Ideas
Warmup:
1. What is the surface area of the cube shown?
Hint: Find the area of each surface.
2. What is the volume of the cube shown?
3. Draw and label all 3-D shapes you can in the space below.
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BASICS of 3-D SHAPES:
Key Words Definition What to look for
Example #1 Example #2
Base
The “bottom” or parallel
polygons on a ________ or the polygon that doesn’t
connect to the apex point on a ____________
Lateral
Having to do with a part of the 3-D shape
that is NOT the _________
All of the lateral parts of a pyramid are what shape?
All of the lateral parts of a prism are what shape?
Prism
2 polygon ______
connected by __________
What shape is the base?
Pyramid
1 polygon ______
connected by ________ to a top _______
This is a ________ pyramid
Face(s)
a flat surface of a _________
or ___________
How many faces? How many edges? How many vertices?
How many faces?
How many edges?
How many vertices?
What is this shape?
Edge(s)
a line segment at the edge of a _________
Vertex
(Vertices)
a corner point of a _________
or a __________
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BIG IDEAS:
Why can’t you just name a shape as a “prism” or a “pyramid?”
What else is required in the name of a 3-D shape?
If a “POLYHEDRON” is only made of polygons, which shapes on this page are NOT polyhedra?
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POLYHEDRON PATTERNS
Complete these charts to discover the polyhedron patterns.
Triangular Prism
Rectangular Prism
Pentagonal Prism
Hexagonal Prism
Base’s # of Sides
# of Faces
# of Vertices
# of Edges
PRISM PATTERNS:
If n=the number of sides on the base shape of the prism, write an algebraic expression for:
the number of faces: ____________________
the number of vertices:___________________
the number of edges: ____________________
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POLYHEDRON PATTERNS Continued
Complete these charts to discover the polyhedron patterns.
Triangular Pyramid
Rectangular Pyramid
Pentagonal Pyramid
Hexagonal Pyramid
Base’s # of Sides
# of Faces
# of Vertices
# of Edges
PYRAMID PATTERNS:
If n=the number of sides on the base shape of the pyramid, write an algebraic expression for:
the number of faces: ____________________
the number of vertices:___________________
the number of edges: ____________________
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DAY 2: Find the SURFACE AREA of rectangular prisms
WARMUP:
Looking at the shape below right, how many faces are there?______
What is the name of this shape?_______________________________
What is the area of each face?
Top:_____________
Bottom:_____________
Left:_______________
Right:______________
Front:_____________
Back:_____________
What do you notice about the areas of the faces?
Can you make a “formula” for the area of a rectangular prism?
*Use dimension names like “length,” “width” and “height.” Variables: l, w, h.
**Make your “l” a cursive loop otherwise it looks like a 1!
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Practice finding SA of rectangular prisms
What is the “FORMULA” for finding SA? SA = ___________________________________
SHAPE L, W, H CALCULATE the SA
l = ________
w = ________
h = ________
SA = _________sq units
l = ________
w = ________
h = ________
SA = _________ cm2
l = ________
w = ________
h = ________
SA = _________ in2
l = ________
w = ________
h = ________
SA = _________ m2
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Day 2 HW: USE a CALCULATOR to find the SA! Use the margins to work them out!
WRITE THE FORMULA HERE: SA = _________________________________
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Day 3: Make or use a NET to find SA by finding the area of each face.
3-D Shape Net of the Shape Area of each face
4x2 = 8 4x3 = 12 4x2 = 8 Surface Area= 3x2 = 6 52 sq units 4x3 = 12 3x2 = 6
Draw in the dimensions on the pyramid
Area of square = ______ Area of triangle = ______ Area of triangle = ______ Area of triangle = ______ Area of triangle = ______ Total Surface Area = _______ cm2
4 in
5 in
3 in
Triangle: ___•___•___=____ Triangle: ___•___•___=____ Rectangle: ___•___=____ Rectangle: ___•___=____ Rectangle: ___•___=____ SA = ______ in2
You draw a net: SA = _________ cm2
You draw a net: SA = ______ in2
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Day 3 HW: USE A CALCULATOR to find the SURFACE AREA…careful…they aren’t all rectangular!
#1
#2
#3
#4
#5
#6
#7
#8
#9
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Day 4: More surface area
Warmup
Cut Nets Stage: 2
The net of a cube has been cut into two. It could be put together in several ways so that it could be folded into a cube.
Here are the nets of 9 solid shapes. Each one of these has been cut into
2 pieces, like the net of the cube.
Can you see which pieces go together?
These are the shapes:
Cube: ___ and ___
Square Pyramid: ___ and ___
Trapezoidal Prism: ___ and ___
Pentagonal Pyramid: ___ and ___
Pentagonal Prism: ___ and ___
Triangular Prism: ___ and ___
Hexagonal Pyramid: ___ and ___
Triangular Pyramid: ___ and ___
Rectangular Prism: ___ and ___
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Day 4: Can we find the SA of combined 3D shapes?
Let’s draw a net of this shape to find the total Surface Area.
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Birdhouse Activity:
Ryan and his father make birdhouses to sell for extra money. All outer surfaces of the birdhouses are painted
bright blue. A half gallon of paint will cover 25 square feet. How many birdhouses could be painted using a
half-gallon of paint?
Questions to consider: Work Space:
1. Paint covers the area in square feet. The birdhouse dimensions are given in inches. How will I represent my dimensions as fractional portions of a foot?
2 inches is ________ft 4 inches is ________ft 6 inches is ________ft 8 inches is ________ ft 10 inches is ________ft 12 inches is ________ft
2. How can I break down the birdhouse into 2-D figures that I know how to calculate the areas of?
8 in
4 in
12 in
10 in
6 in
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3. Label the measures of each part of the birdhouse shape. Then find the AREA of each shape.
4. What is the TOTAL SA? __________ ft2 5. If a half gallon of paint will cover 25 ft2, how many birdhouses can be painted with a half gallon of paint?
Roof sections: Lower portions:
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Day 5: How can I calculate the VOLUME of prisms?
Surface Area is on the ____________________ of a 3-D shape.
Volume is on the _____________________ of a 3-D shape.
Volume is MUCH EASIER than Surface Area because to calculate it you simply
find:
Volume = Area of Base Shape • height of 3-D shape
V = Bh
Let’s practice with different 3-D shapes:
Shape Base Shape Dimensions and
Area SHADE the BASE
Height of
3-D shape
Calculate the VOLUME
V = Bh
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Day 5: Homework…Yes, you may use a calculator but show what you typed! There is margin space to help show work!
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Day 6: Practice with V
Warmup:
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Day 6: Practice Problems involving VOLUME to solve with your table:
1. What is the volume of a rectangular prism with a length of 5 m, a width of 6 m, and a height of 12 m?
2. What is the height of a rectangular prism with a length of 10 in., a width of 3 in., and a volume of 210 in.2?
3. What is the volume of a cube with an edge that measures 4 cm?
4. What is the volume of a triangular prism with a height of 6 ft. and a base shape with dimensions 3 ft x 6 ft?
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Day 6 HW
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Day 7: What do I do in finding VOLUME if the edges of a rectangular prism are fractions?
A right rectangular prism has edges of 1 ”, 1” and 1 ”. How
many cubes with side lengths of would be needed to fill the
prism? What is the volume of the prism?
Woah…let’s break this down!
Step 1: Remember the birdhouse when we converted inches into feet? Well, here we
need to convert our measures into quarters…so
11
4=
4 1 =
4 1
1
2 =
2=
4
Step 2: If each measure is “fourths” I can draw how many “fourth of a cube” edges
there area on each side.
11
2 =
4
1 = 4
11
4 =
4
Step 3: Using “fourths of cubes,” how many blocks are at each dimension?
Fill these in below:
_____ • _____ • _____ = _____
4 4 4 4
So, how many blocks that are “fourths” are in the volume? _______________
Step 4: Calculate the Volume w/o a calculator:V = ___________ = ___________ = _____ in3
1
4
1
2
1
4
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Day 7: Volume of Prism with Fractional Edge Practice
1. A rectangular container has a length of 6 inches, a width of 2 ½ inches, and height of 4 ¼ inches. What is the Volume?
2. A follower box is 4ft. long, 23
4 ft. wide, and ½ ft. deep. How many cubic feet of
dirt can it hold?
3. Explain why the volume of a cube with side lengths 11
2in, 1
1
2in , 1
1
2in is 9
1
8 𝑖𝑛3.
Draw the diagram to match this prism.
Page 24 CCM6 UNIT 12 SA and V
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Day 7 HW: Volume Fractional Edge Length Word Problems
1. A right rectangular prism has edges of, 21
4 in, 2 in and 1
1
2in. How many cubes with lengths of
1
4in
would be needed to fill the prism? What is the volume?
2. Find the volume of a rectangular prism with dimensions 11
2 in , 1
1
2 in and 2
1
2 in .How many cubes
with lengths of 1
2 in would be needed to fill the prism?
3. A follower box is 3feet long, 1 3
4 feet wide, and
1
2 feet deep. How many cubic feet of dirt can it
hold?
4. Draw a diagram to match the rectangular prism whose length is 51
2in, width is 4in and height is
41
2in.
5. Use centimeter grid papers to build a rectangular prism with the volume of 24 cubic units. At least
one of the side lengths of the prism is a fractional unit. What are the dimensions of the rectangular
prisms you built? What is the surface area of the prism?
6. Mr. White is trying to store boxes in a storage room with length of 8yd, width of 5yd and height of
2yd. How many boxes can fit in this space if each is box is 21
4 feet long 1
1
2 feet wide and 1 feet deep
?
7. Linda keeps her jewelry in a box with dimensions 81
4 in by 3
3
4 in by 4in. Find the volume of
Linda’s jewelry box.
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