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Objective

Find the volumes of prisms and cylinders

Prism Volume = Area of base height of figure

Cylinder Volume

Vocabulary

Volume

The number of cubic units needed to fill the space occupied by a solid

Vocabulary

Cylinder

A solid whose bases are congruent, parallel circles, connected with a curved side

Vocabulary

Complex solid

An object made up of more than one type of solid

Example 1 Find the Volume of a Rectangular Prism

Example 2 Find the Volume of a Triangular Prism

Example 3 Find the Volumes of Cylinders

Example 4 Find the Volumes of Cylinders

Example 5 Find the Volume of a Complex Solid

Find the volume of the prism.

The prism has a rectangular base

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Volume = Area of base Height of prism

Remember: The top and base have the same dimensions on a prism

Replace formula for rectangle in “area of base”

V = (L W) Height of prism

Note: Area of base is in parenthesis because area must be figured first

Find the volume of the prism.

Replace L with 7 in

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Volume = Area of base Height of prism

V = (L W) Height of prism

V = (7 in

Replace W with 5 in

5 in)

Replace Height of prism with 11 in

11 in

Follow order of operations P E MD AS

Work inside parenthesis

Find the volume of the prism.

Multiply 7 in 5 in

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Volume = Area of base Height of prism

V = (L W) Height of prism

V = (7 in 5 in) 11 in

V = 35 in2 11 in Multiply 35 in2 5 in

V = 385 in3 Answer:

Find the volume of the prism.

Answer: V = 120 in3

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Find the volume of the prism.

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Volume = Area of base Height of prism

The prism has a triangular base

Note: The base does not have to be on the bottom

Replace formula for triangle in “area of base”

Volume = ( bh) Height of prism

Find the volume of the prism.

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Volume = Area of base Height of prism

Replace b with base of triangle which is 15 ft

Volume = ( bh) Height of prism

Volume = ( 15 ft

Replace h with height of triangle which is 9 ft

9 ft)

Replace height of prism with 4 ft

4 ft

Find the volume of the prism.

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Volume = Area of base Height of prism

Volume = ( bh) Height of prism

Volume = ( 15 ft 9 ft) 4 ft Follow order of operations P E MD ASWork inside parenthesis

Multiply 15 ft 9 ft

Volume = 67.5 ft2 4 ft

Multiply 67.5 ft2 4 ft

Volume = 270 ft3 Answer:

Find the volume of the prism.

Answer: V = 45 ft3

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Find the volume of the cylinder.

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Volume = Area of base Height of prism

The prism has a circle base

Replace formula for circle in “area of base”

Volume = ( r2) Height of prism

Replace r with 3 cm

Volume = ( [3 cm]2)

Note: Put 3 cm in enclosures because must square both number and unit of measure

Find the volume of the cylinder.

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Volume = Area of base Height of prism

Replace height of prism with 12 cm

Volume = ( r2) Height of prism

Volume = ( [3 cm]2) 12 cm

Follow order of operations P E MD AS

Work inside parenthesis that are inside the parenthesis!

Find the volume of the cylinder.

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Volume = Area of base Height of prism

Multiply 3 cm 3 cm

Volume = ( r2) Height of prism

Volume = ( [3 cm]2) 12 cm

Volume = ( 9 cm2) 12 cm

Multiply 9 cm2 Volume = 28.26 cm2 12 cm

Do not clear display on calculator

Multiply 28.26 cm2 12 cm

Volume = 339.29 cm3 Answer:

Find the volume of the cylinder.

Answer: V = 169.56 in3

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Find the volume of the cylinder.

diameter of base, 18 yd; height, 25.4 yd

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Volume = Area of base Height of prism

A cylinder has a circle base

Replace formula for circle in “area of base”

Volume = ( r2) Height of prism

Replace r with 9 yd

Remember: radius is half the diameter

Volume = ( [9 yd]2)

Find the volume of the cylinder.

diameter of base, 18 yd; height, 25.4 yd

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Volume = Area of base Height of prism

Volume = ( r2) Height of prism

Volume = ( [9 yd]2)

Replace height of prism with 25.4 yd

25.4 yd

Follow order of operations P E MD ASWork inside parenthesis that are inside the parenthesis!

Find the volume of the cylinder.

diameter of base, 18 yd; height, 25.4 yd

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Volume = Area of base Height of prism

Volume = ( r2) Height of prism

Volume = ( [9 yd]2) 25.4 yd Multiply 9 yd 9 yd

Volume = ( 81 yd2) 25.4 yd Multiply 81 yd2

Do not clear display on calculator

Multiply 254.34 yd2 25.4 yd

Volume = 254.34 yd2 25.4 yd

Volume = 6,460.24 yd3Answer:

Find the volume of the cylinder.

diameter of base, 8 yd; height, 10 yd

Answer: V = 502.40 yd3

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TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.

Identify each shape

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The big shape is a rectangular prism

The hole in the box is a cylinder

Find the area of each shape and subtract the cylinder from the rectangular prism

TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.

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Volume = Area of base Height of prism

Replace formula for circle in “area of base”

Rectangular Prism:

V = (L W) Height of prism

Replace L with 4 cm

V = (4 cm

Replace W with 3 cm

3 cm)

TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.

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Volume = Area of base Height of prism

Replace height of prism with 6 cm

Rectangular Prism:

V = (L W) Height of prism

V = (4 cm 3 cm) 6 cm

Follow order of operations P E MD AS

Work inside parenthesis

TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.

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Volume = Area of base Height of prism

Multiply 4 cm 3 cm

Rectangular Prism:

V = (L W) Height of prism

V = (4 cm 3 cm) 6 cm

V = 12 cm2 6 cm Multiply 12 cm2 6 cm

V = 72 in3

TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.

5/5

Volume = Area of base Height of prism

Cylinder:

Replace formula for circle in “area of base”

Volume = ( r2) Height of prism

Replace r with 1 cm

Volume = ( [1 cm]2)

Replace height of prism with 3 cm

3 cm

TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.

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Volume = Area of base Height of prism

Cylinder:

Volume = ( r2) Height of prism

Volume = ( [1 cm]2) 3 cmFollow order of operations P E MD AS

Work inside parenthesis that are inside the parenthesis!

TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.

5/5

Volume = Area of base Height of prism

Cylinder:

Volume = ( r2) Height of prism

Volume = ( [1 cm]2) 3 cm

Multiply 1 cm 1 cmVolume = ( 1 cm2) 3 cmMultiply 1 cm2 Volume = 3.14 cm2 3 cmDo not clear display on calculator

TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.

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Volume = Area of base Height of prism

Cylinder:

Volume = ( r2) Height of prism

Volume = ( [1 cm]2) 3 cm

Volume = ( 1 cm2) 3 cm

Volume = 3.14 cm2 3 cm

Multiply 3.14 cm2 3 cm

Volume = 9.42 cm3

Rectangular Prism Cylinder

Subtract the volume of cylinder from volume of prism

V = 62.58 cm3Answer:

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V = 9.42 cm3 V = 72 in3

V = 72 in3 - 9.42 cm3

HOBBIES A small wooden cube has been glued to a larger wooden block for a whittling project. What is the volume of the wood to be whittled?

Answer:

*

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Assignment

Lesson 7:5Volume of Prisms and

Cylinders4 - 23 All