10.7 Volume of Prisms
6.4.5 I can find the volume in
rectangular and triangular
prisms
Warm Up
Find the area of each figure. Use 3.14
for .
1. rectangle with base length 8 in. and
height 12 in. 96 in2
2. circle with diameter 8 ft 50.24 ft2
Volume is the number of cubic
units needed to fill a space.
To find the volume of prisms you simply
multiply the area of the base times the height.
V = area of base x height
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.
V = 3,718 in3
16 in.
12 in.
29 in.
V = 5,568 in3
V = 10.14 m3
Find the volume of the triangular prism.
V = 136.5 ft3
7m
1.6 m
4.2 m
V = Bh
V = 23.52 m3
Find the volume of each figure.
1. rectangular prism with length 20 cm, width
15 cm, and height 12 cm 3,600 cm3
2. triangular prism with a height of 12 cm and a
triangular base with base length 7.3 cm and
height 3.5 cm 153.3 cm3
3. Find the volume of the figure shown.
38.13 cm3
Identify the volume of a rectangular prism with
length 25 cm, width 20 cm, and height 10 cm.
A. 5,000 cm3
B. 5,225 cm3
C. 5,450 cm3
D. 5,650 cm3
Identify the volume of the figure shown.
A. 72.52 cm3
B. 63.64 cm3
C. 62.5 cm3
D. 61.67 cm3
10.8 Volume of Cylinders
6.4.5 I can find the volumes of
cylinders
Warm Up
Find the volume of each figure described.
1. rectangular prism with length 12 cm,
width 11 cm, and height 10 cm
1,320 cm3
2. triangular prism with height 11 cm and
triangular base with base length 10.2 cm and
height 6.4 cm
359.04 cm3
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.
Find the volume V of the cylinder to the
nearest cubic unit.
V = r2h
V  351.68
The volume is about 352 ft3.
Find the volume V of the cylinder to the nearest cubic
unit.
V  863.5
The volume is about 864 cm3.
Find the volume V of the cylinder to the
nearest cubic unit.
6 ft
5 ft
V  565.2
The volume is about 565 ft3.
8 cm
6 cm
V  301.44
The volume is about 301 cm3.
h
r= 4 +5
h = 8 in
V  1,230.88
The volume is about 1,231 in3.
V  1,384.74
The volume is about 1,385 in3.
Find which cylinder has the greater volume.
Cylinder 1:
V  84.78 cm3
Cylinder 2:
V  169.56 cm3
Cylinder 2 has the greater volume because
169.56 cm3 > 84.78 cm3.
Find which cylinder has the greater volume.
Cylinder 1:
10 cm
2.5 cm
V  196.25 cm3
Cylinder 2:
4 cm
4 cm
V  50.24 cm3
Cylinder 1 has the greater volume because
196.25 cm3 > 50.24 cm3.
Lesson Quiz for Student Response Systems
1. Identify the volume of a cylinder with a
radius of 11 ft and a height of 5 ft to the
nearest cubic unit. Use 3.14 for .
A. 1,900 ft3
B. 1,890 ft3
C. 1,706 ft3
D. 690 ft3
Lesson Quiz for Student Response Systems
2. Identify the volume of a cylinder with a
radius of 4.3 ft and a height of 5 ft to the
nearest cubic unit. Use 3.14 for .
A. 338 ft3
B. 305 ft3
C. 297 ft3
D. 290 ft3