Geometry Section 12-4

Section 12-4
Volumes of Prisms and Cylinders

Essential Questions
• How do you ﬁnd volumes of prisms?
• How do you ﬁnd volumes of cylinders?

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

Volume of a Prism
V = Bh
B = area of the base

Volume of a Prism
V = Bh
B = area of the base
h = height of the prism

Example 1
Find the volume of the prism.

Example 1
V = Bh

Example 1
V = Bh
B = area of the
triangle base

Example 1
V = Bh
B = area of the
triangle base
V = 1
2 (10)(12)(25)

Example 1
V = Bh
B = area of the
triangle base
V = 1
2 (10)(12)(25)
V = 1500 cm3

Volume of a Cylinder
V = Bh or V = πr2
h

V = Bh or V = πr2
h
B = area of the base: B = πr2

h = height of the cylinder
V = Bh or V = πr2
h
B = area of the base: B = πr2

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

Example 2
V = πr2
h

Example 2
V = πr2
h
V = π(8)2
(22)

Example 2
V = πr2
h
V = π(8)2
(22)
V = 1408π

Example 2
V = πr2
h
V = π(8)2
(22)
V = 1408π
V ≈ 4423.36 mm3

Example 3
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 3
V = πr2
h

Example 3
V = πr2
h
V = π(8)2
(22)

Example 3
V = πr2
h
V = π(8)2
(22)
V = 1408π

Example 3
V = πr2
h
V = π(8)2
(22)
V = 1408π
V ≈ 4423.36 mm3

Example 4

Example 4
V = Bh

Example 4
V = Bh
V = (13)(10)(17)

Example 4
V = Bh
V = (13)(10)(17)
V = 2210 in3

Example 5
Prisms 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 5
Prism A Prism B
Prism A

Example 5
V = (4)(x)(5)
Prism A Prism B
Prism A

Example 5
V = (4)(x)(5)
Prism A Prism B
Prism A
V = 20x

Example 5
V = (4)(x)(5)
Prism A Prism B
Prism A
V = 20x
Prism B

Example 5
V = (4)(x)(5)
Prism A Prism B
Prism A
V = 20x
V = (4)(x)(9)
Prism B

Example 5
V = (4)(x)(5)
Prism A Prism B
Prism A
V = 20x
V = (4)(x)(9)
Prism B
V = 36x

Example 5
Prism B = Prism A+128
Prism A Prism B

Example 5
Prism A Prism B
36x = 20x +128

Example 5
Prism A Prism B
36x = 20x +128
−20x−20x

Example 5
Prism A Prism B
36x = 20x +128
16x = 128
−20x−20x

Example 5
Prism A Prism B
36x = 20x +128
16x = 128
−20x−20x
16 16

Example 5
Prism A Prism B
36x = 20x +128
16x = 128
−20x−20x
16 16
x = 8

Example 5
Prism A Prism B
36x = 20x +128
16x = 128
−20x−20x
16 16
x = 8
The length of each prism is 8 inches.

Problem Set
p. 850 #1-12,16-19 all; skip #4
“It is never too late to be what you might have been.”
- George Eliot

Geometry Section 12-4

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