Section 12-4Volumes of Prisms and Cylinders

Essential Questions

• How do you find volumes of prisms?

• How do you find volumes of cylinders?

Vocabulary Refresh

1.Volume:

Vocabulary Refresh

1.Volume: The amount of space inside a three-dimensional object

Volume of a Prism

Volume of a Prism

V = Bh

Volume of a Prism

V = BhB = area of the base

Volume of a Prism

V = BhB = area of the base

h = height of the prism

Example 1Find the volume of the prism.

Example 1Find the volume of the prism.

V = Bh

Example 1Find the volume of the prism.

V = Bh

B = area of the triangle base

Example 1Find the volume of the prism.

V = Bh

B = area of the triangle base

V = 12 (10)(12)(25)

Example 1Find the volume of the prism.

V = Bh

B = area of the triangle base

V = 12 (10)(12)(25)

V =1500 cm3

Volume of a Cylinder

Volume of a Cylinder

V = Bh or V = πr 2h

Volume of a Cylinder

V = Bh or V = πr 2h

B = area of the base: B = πr 2

Volume of a Cylinder

h = height of the cylinder

V = Bh or V = πr 2h

B = area of the base: B = πr 2

Example 2Find the volume of the cylinder to the nearest hundredth.

Example 2Find the volume of the cylinder to the nearest hundredth.

V = πr 2h

Example 2Find the volume of the cylinder to the nearest hundredth.

V = πr 2h

V = π(8)2(22)

Example 2Find the volume of the cylinder to the nearest hundredth.

V = πr 2h

V = π(8)2(22)

V =1408π

Example 2Find the volume of the cylinder to the nearest hundredth.

V = πr 2h

V = π(8)2(22)

V =1408π

V ≈ 4423.36 mm3

Example 3Find the volume of the cylinder to the nearest hundredth.

For an oblique prism or cylinder, it’s the same process! Make sure you use the height of the prism/cylinder (perpendicular

distance between bases)!

Example 3Find the volume of the cylinder to the nearest hundredth.

V = πr 2h

For an oblique prism or cylinder, it’s the same process! Make sure you use the height of the prism/cylinder (perpendicular

distance between bases)!

Example 3Find the volume of the cylinder to the nearest hundredth.

V = πr 2h

V = π(8)2(22)

For an oblique prism or cylinder, it’s the same process! Make sure you use the height of the prism/cylinder (perpendicular

distance between bases)!

Example 3Find the volume of the cylinder to the nearest hundredth.

V = πr 2h

V = π(8)2(22)

V =1408π

For an oblique prism or cylinder, it’s the same process! Make sure you use the height of the prism/cylinder (perpendicular

distance between bases)!

Example 3Find the volume of the cylinder to the nearest hundredth.

V = πr 2h

V = π(8)2(22)

V =1408π

V ≈ 4423.36 mm3

For an oblique prism or cylinder, it’s the same process! Make sure you use the height of the prism/cylinder (perpendicular

distance between bases)!

Example 4Find the volume of the prism.

Example 4Find the volume of the prism.

V = Bh

Example 4Find the volume of the prism.

V = Bh

V = (13)(10)(17)

Example 4Find the volume of the prism.

V = Bh

V = (13)(10)(17)

V = 2210 in3

Example 5Prisms A and B have the same width and length, but different heights. If the volume of prism B is 128 cubic inches greater than the volume of prism A, what is the length of each prism?

Prism A Prism B

Example 5Prisms A and B have the same width and length, but different heights. If the volume of prism B is 128 cubic inches greater than the volume of prism A, what is the length of each prism?

Prism A Prism B

Prism A

Example 5Prisms A and B have the same width and length, but different heights. If the volume of prism B is 128 cubic inches greater than the volume of prism A, what is the length of each prism?

V = (4)(x)(5)

Prism A Prism B

Prism A

Example 5Prisms A and B have the same width and length, but different heights. If the volume of prism B is 128 cubic inches greater than the volume of prism A, what is the length of each prism?

V = (4)(x)(5)

Prism A Prism B

Prism A

V = 20x

Example 5Prisms A and B have the same width and length, but different heights. If the volume of prism B is 128 cubic inches greater than the volume of prism A, what is the length of each prism?

V = (4)(x)(5)

Prism A Prism B

Prism A

V = 20xPrism B

Example 5Prisms A and B have the same width and length, but different heights. If the volume of prism B is 128 cubic inches greater than the volume of prism A, what is the length of each prism?

V = (4)(x)(5)

Prism A Prism B

Prism A

V = 20x

V = (4)(x)(9)Prism B

Example 5Prisms A and B have the same width and length, but different heights. If the volume of prism B is 128 cubic inches greater than the volume of prism A, what is the length of each prism?

V = (4)(x)(5)

Prism A Prism B

Prism A

V = 20x

V = (4)(x)(9)Prism B

V = 36x

Example 5Prisms A and B have the same width and length, but different heights. If the volume of prism B is 128 cubic inches greater than the volume of prism A, what is the length of each prism?

Prism A Prism B

Example 5Prisms A and B have the same width and length, but different heights. If the volume of prism B is 128 cubic inches greater than the volume of prism A, what is the length of each prism?

Prism B = Prism A+128

Prism A Prism B

Example 5Prisms A and B have the same width and length, but different heights. If the volume of prism B is 128 cubic inches greater than the volume of prism A, what is the length of each prism?

Prism B = Prism A+128

Prism A Prism B

36x = 20x +128

Example 5Prisms A and B have the same width and length, but different heights. If the volume of prism B is 128 cubic inches greater than the volume of prism A, what is the length of each prism?

Prism B = Prism A+128

Prism A Prism B

36x = 20x +128−20x−20x

Example 5Prisms A and B have the same width and length, but different heights. If the volume of prism B is 128 cubic inches greater than the volume of prism A, what is the length of each prism?

Prism B = Prism A+128

Prism A Prism B

36x = 20x +128

16x =128−20x−20x

Example 5Prisms A and B have the same width and length, but different heights. If the volume of prism B is 128 cubic inches greater than the volume of prism A, what is the length of each prism?

Prism B = Prism A+128

Prism A Prism B

36x = 20x +128

16x =128−20x−20x

16 16

Example 5Prisms A and B have the same width and length, but different heights. If the volume of prism B is 128 cubic inches greater than the volume of prism A, what is the length of each prism?

Prism B = Prism A+128

Prism A Prism B

36x = 20x +128

16x =128−20x−20x

16 16x = 8

Example 5Prisms A and B have the same width and length, but different heights. If the volume of prism B is 128 cubic inches greater than the volume of prism A, what is the length of each prism?

Prism B = Prism A+128

Prism A Prism B

36x = 20x +128

16x =128−20x−20x

16 16x = 8

The length of each prism is 8 inches.

Problem Set

Problem Set

p. 850 #1-12,16-19 all; skip #4

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