# Volume of Prisms and Cylinders HW Notes

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VOCABULARY
Volume is the number of cubic
units needed to fill a space.
Introduction
You need 10, or 5 &middot; 2,
centimeter cubes to cover
the bottom layer of this
rectangular prism.
You need 3 layers of 10
cubes each to fill the prism.
It takes 30, or 5 &middot; 2 &middot; 3,
cubes.
Volume is expressed in cubic units, so the volume
of the prism is 5 cm &middot; 2 cm &middot; 3 cm = 30 cm3.
Example 1: Finding the Volume of a
Rectangular Prism
Find the volume of the rectangular prism.
Example 2
Find the volume of each rectangular prism.
3
Example 3
Find the volume of each rectangular prism.
V = lwh
=1&times;1&times;2
= 2 km3
Example 4: Finding the Volume of a Triangular
Prism
Find the volume of the
triangular prism.
V = Bh
1
__
V = ( • 3.9
2
•
V = 10.14 m3
1.3)
•
4
Write the formula.
1
B = __ • 3.9 • 1.3; h = 4.
2
Multiply.
Example 4
Example 5
1 m
2
Example 6
Example 7
A toy box is a rectangular prism that is 3 ft long,
2 feet wide, and 2 feet tall. Another toy box has
the same dimensions, except that it is longer. If
the longer toy box has a volume that is 50%
greater than the original toy box, what is the
length of the longer toy box?
FYI
To find the volume of a cylinder, you can use
the same method as you did for prisms:
Multiply the area of the base by the height.
volume of a cylinder = area of base  height
The area of the circular base is r2, so the
formula is V = Bh = r2h.
Example 8: Finding the Volume of a Cylinder
Find the volume V of the cylinder to the
nearest cubic unit.
r = 4 ft, h = 7 ft
Example 9: Finding the Volume of a Cylinder
h +4
__
r=
in., h = 9 in.
3
Example 10
Find the volume V of each cylinder to the
nearest cubic unit.
r = 6 ft, h = 5 ft
Example 11
h
r = 4 + 5, h = 8 in.
Example 12
Sara has a cylinder-shaped sunglasses case with a
3 in. diameter and a height of 6 in. Ulysses has a
cylinder-shaped pencil holder with a 4 in. diameter
and a height of 7 in. Estimate the volume of each
cylinder to the nearest cubic inch.
Sara’s sunglasses case
Example 13
Ulysses’ pencil holder
Example 14: Comparing Volumes of Cylinders
Find which cylinder has the greater volume.
Cylinder 1:
Cylinder 2:
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