REVIEW & PRACTICE
for the Test
Volume is the number of cubic
units needed to fill a space.
It takes 10, or 5 · 2,
centimeter cubes to cover
the bottom layer of this
rectangular prism.
There are 3 layers of 10
cubes each. It takes 30, or
5 · 2 · 3, cubes to fill the
prism.
The volume of the prism is 5 cm · 2 cm · 3 cm = 30 cm3.
Additional Example 1: Finding the Volume of a
Rectangular Prism
Find the volume of the rectangular prism.
13 in.
26 in.
11 in.
V = lwh
V = 26
•
Write the formula.
11
•
V = 3,718 in3
13
l = 26; w = 11; h = 13
Multiply.
Try This: Example 1
Find the volume of the rectangular prism.
16 in.
29 in.
12 in.
V = lwh
V = 29
•
Write the formula.
12
•
V = 5,568 in3
16
l = 29; w = 12; h = 16
Multiply.
To find the volume of any prism,
you can use the formula V= Bh,
where B is the area of the base,
and h is the prism’s height. So, to
find the volume of a triangular
prism, B is the area of the
triangular base and h is the height
of the prism.
Additional Example 2A: Finding the Volume of
a Triangular Prism
Find the volume of each triangular prism.
A.
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.
Additional Example 2B: Finding the Volume of
a Triangular Prism
Find the volume of the triangular prism.
B.
V = Bh
1
__
V = ( • 6.5
2
V = 136.5 ft
3
•
7)
•
6
Write the formula.
1
B = __ • 6.5 • 7; h = 6.
2
Multiply.
Try This: Example 2A
Find the volume of each triangular prism.
A.
7m
1.6 m
4.2 m
V = Bh
1
__
V = ( • 4.2
2
•
V = 23.52 m3
1.6)
•
7
Write the formula.
1
B = __ • 4.2 • 1.6; h = 7.
2
Multiply.
Try This: Example 2B
Find the volume of each triangular prism.
B.
9 ft
5 ft
4.5 ft
V = Bh
1
__
V = ( • 4.5
2
•
V = 101.25 ft3
9)
•
5
Write the formula.
1
B = __ • 4.5 • 9; h = 5.
2
Multiply.
Learn to find volumes of cylinders.
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.
Additional Example 1A: Finding the Volume of
a Cylinder
Find the volume V of the cylinder to the
nearest cubic unit.
A.
V = r2h
Write the formula.
V  3.14  42  7
Replace  with 3.14, r with
4, and h with 7.
Multiply.
V  351.68
The volume is about 352 ft3.
Additional Example 1B: Finding the Volume of a
Cylinder
B.
10 cm ÷ 2 = 5 cm
Find the radius.
V = r2h
Write the formula.
V  3.14  52  11
Replace  with 3.14, r with
5, and h with 11.
Multiply.
V  863.5
The volume is about 864 cm3.
Additional Example 1C: Finding the Volume of a
Cylinder
C.
h +4
r = __
3
9 +4=7
r = __
3
V = r2h
V  3.14  72  9
V  1,384.74
Find the radius.
Substitute 9 for h.
Write the formula.
Replace  with 3.14, r with
7, and h with 9.
Multiply.
The volume is about 1,385 in3.
What is a Right Triangle?
a
c
b
• The Pythagorean Theorem
applies only to right triangles.
• A right triangle is a triangle
that has a 90 degree right
angle. It has two legs and a
hypotenuse.
• The hypotenuse is the side
opposite the right angle and
is always the longest.
• The variables a + b are used
for the legs and c is the