Transcript Slide 1

Volume of Prisms and
Cylinders
The volume of a three-dimensional figure is the
number of nonoverlapping unit cubes of a given size
that will exactly fill the interior.
OR
Volume is how much cubic space a figure will hold
Example 1A: Finding Volumes of Prisms
Find the volume of
the prism. Round to
the nearest tenth, if
necessary.
Volume of a right rectangular prism
V = ℓwh
= (13)(3)(5) Substitute 13 for ℓ, 3 for w, and 5 for h.
= 195 cm3
Example 1B: Finding Volumes of Prisms
Find the volume of a cube with edge length 15
in. Round to the nearest tenth, if necessary.
V = s3
= (15)3
= 3375 in3
Volume of a cube
Substitute 15 for s.
Example 2: Recreation Application
A swimming pool is a rectangular prism.
Estimate the volume of water in the pool.
Example 2 Continued
Find the volume of the swimming pool in cubic feet.
V = ℓwh = (25)(15)(19) = 3375 ft3
Check It Out! Example 2
What if…? Estimate the volume if the height
were doubled.
Find the volume of the
aquarium in cubic feet.
V = ℓwh = (120)(60)(16) = 115,200 ft3
Cavalieri’s principle
also relates to cylinders.
The two stacks have
the same number of
CDs, so they have
the same volume.
Example 3A: Finding Volumes of Cylinders
Find the volume of the
cylinder. Give your answers
in terms of  and rounded to
the nearest tenth.
V = r2h
Volume of a cylinder
= (9)2(14)
= 1134 in3  3562.6 in3
Check It Out! Example 3
Find the volume of a cylinder with a diameter of
16 in. and a height of 17 in. Keep your answer
in terms of .
V = r2h
Volume of a cylinder
= (8)2(17) Substitute 8 for r and 17 for h.
= 1088 in3  3418.1 in3
Example 4: Exploring Effects of Changing Dimensions
The radius and height of the
cylinder are multiplied by .
Describe the effect on the
volume.
original dimensions:
radius and height
multiplied by :
Example 4 Continued
The radius and height of the
cylinder are multiplied by .
Describe the effect on the
volume.
Notice that
. If the radius and
height are multiplied by
by
, or
.
, the volume is multiplied
Volume of Cones
Example: Finding Volumes of Cones
Find the volume of a cone with radius 7 cm and
height 15 cm. Give your answers both in terms
of  and rounded to the nearest tenth.
Volume of a pyramid
Substitute 7 for r and 15 for h.
= 245 cm3 ≈ 769.7 cm3
Simplify.
Check It Out! Example 3
Find the volume of the cone.
Volume of a cone
Substitute 9 for r and 8 for h.
≈ 216 m3 ≈ 678.6 m3 Simplify.
Homework
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Page 83, #3, 5
Page 85, #13
Page 86, #15, 17
Page 87, #20, 21, 26
Page 88, #29
Page 89, #37a, 38a