1. Calculate Volume of Prisms & Cylinders
9.4
Calculate Volume of Prisms & Cylinders

2. V = Bh Where B = area of the base And h = height
Volume of a Prism
V = Bh Where B = area of the base And h = height

3. Find the volume of the box by determining
Example 1
Find the Volume of a Rectangular Prism
Find the volume of the box by determining
how many unit cubes fit in the box.
SOLUTION
The base is 5 units by 3 units. So, 3 · 5, or 15 unit cubes are needed to cover the base layer.
There are 4 layers. Each layer has 15 cubes. So, the total number of cubes is 4 · 15, or 60.
ANSWER
The volume of the box is 60 cubic units. 3

4. Find the volume of the prism.
Example 2
Find the Volume of a Prism
Find the volume of the prism. a. b.
SOLUTION a.
V = Bh
Write the formula for volume of a prism.
= (7 · 4) · 5
Area of rectangular base = l · w = 7 · 4.
= 140
Simplify.
ANSWER
The volume is 140 cubic inches. 4

5. Write the formula for volume of a prism. Area of triangular base =
Example 2
Find the Volume of a Prism b.
V = Bh
Write the formula for volume of a prism.
Area of triangular base = 1 2 –
· 8 · 6. =
· 8 · 6 · 3
= 72
Simplify.
ANSWER
The volume is 72 cubic feet. 5

6. Find the volume of the prism.
Checkpoint
Find Volume of Prisms 2.
Find the volume of the prism. 1. 3.

7. Find the volume of the prism.
Checkpoint
Find Volume of Prisms
Find the volume of the prism. 1.
ANSWER
216 ft3 2.
ANSWER
125 cm3 3.
ANSWER
245 in.3

8. Volume of a Cylinder
V = πr2h

9. How do the radius and height of the mug compare to the radius
Example 3
Compare Volumes of Cylinders
How do the radius and height of
the mug compare to the radius
and height of the dog bowl? a.
How many times greater is the
volume of the bowl than the
volume of the mug? b.
SOLUTION
The radius of the mug is 2 inches and the radius of the dog bowl is 6 inches. The radius of the bowl is three times the radius of the mug. The height of the mug is the same as the height of the bowl. a. 9

10. Write the formula for volume. Substitute for r and for h.
Example 3
Compare Volumes of Cylinders b.
Volume of mug
Volume of dog bowl
V = πr2h
Write the formula for volume.
= π(22)(4)
= π(62)(4)
Substitute for r and for h.
= 16π
Simplify.
= 144π
To compare the volume of the bowl to the volume of the mug, divide the volume of the bowl by the volume of the mug.
––––––––––––––
Volume of bowl
Volume of mug
144π
16π
––––– =
= 9
ANSWER
The volume of the bowl is nine times the volume of the mug. 10

11. Checkpoint
Find Volume of Cylinders
Find the volume of the cylinder. Round your answer to the nearest whole number. 6. 4. 5.

12. Checkpoint
Find Volume of Cylinders
Find the volume of the cylinder. Round your answer to the nearest whole number. 4.
ANSWER
38 ft3 5.
ANSWER
16 in.3 6.
ANSWER
126 m3

13. Review
Find the surface area of the solid. If necessary, round your answer to the nearest whole number. 1.
150 m2
ANSWER 2.
2286 mm2
ANSWER

14. Find the lateral area of a right cone with radius 5 inches and slant height 22 inches. Round your answer to the nearest whole number. 3.
346 in.2
ANSWER

15. Worksheet 9.4A