1. Volume of Cylinders Notes
10-8
Volume of Cylinders Notes
Course 1

2. Course 1
10-8
Volume 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.

3. Additional Example 1A: Finding the Volume of a Cylinder
Course 1
10-8
Volume of Cylinders
Additional Example 1A: Finding the Volume of a Cylinder
Find the volume V of the cylinder to the nearest cubic unit.
V = r2h
Write the formula.
V  3.14  42  7
Replace  with 3.14, r with 4, and h with 7.
V 
Multiply.
The volume is about 352 ft3.

4. Additional Example 1B: Finding the Volume of a Cylinder
Course 1
10-8
Volume of Cylinders
Additional Example 1B: Finding the Volume of a Cylinder
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.
V  863.5
Multiply.
The volume is about 864 cm3.

5. Additional Example 1C: Finding the Volume of a Cylinder
Course 1
10-8
Volume of Cylinders
Additional Example 1C: Finding the Volume of a Cylinder
r = h 3 __
Find the radius.
r = = 7 9 3 __
Substitute 9 for h.
V = r2h
Write the formula.
V  3.14  72  9
Replace  with 3.14, r with 7, and h with 9.
V  1,384.74
Multiply.
The volume is about 1,385 in3.

6. Volume of Cylinders 10-8 Check It Out: Example 1A
Course 1
10-8
Volume of Cylinders
Check It Out: Example 1A
Find the volume V of each cylinder to the nearest cubic unit.
6 ft
5 ft
V = r2h
Write the formula.
V  3.14  62  5
Replace  with 3.14, r with 6, and h with 5.
V  565.2
Multiply.
The volume is about 565 ft3.

7. Volume of Cylinders 10-8 Check It Out: Example 1B 8 cm 6 cm
Course 1
10-8
Volume of Cylinders
Check It Out: Example 1B
8 cm
6 cm
8 cm ÷ 2 = 4 cm
Find the radius.
V = r2h
Write the formula.
V  3.14  42  6
Replace  with 3.14, r with 4, and h with 16.
V 
Multiply.
The volume is about 301 cm3.

8. Volume of Cylinders 10-8 Check It Out: Example 1C h r = + 5 4 h = 8 in
Course 1
10-8
Volume of Cylinders
Check It Out: Example 1C h
r = 4
h = 8 in
r = h 4 __
Find the radius.
r = = 7 8 4 __
Substitute 8 for h.
V = r2h
Write the formula.
V  3.14  72  8
Replace  with 3.14, r with 7, and h with 8.
V 
Multiply.
The volume is about 1,231 in3.

9. Course 1
10-8
Volume of Cylinders
Additional Example 3: Comparing Volumes of Cylinders Find which cylinder has the greater volume.
Cylinder 1:
V = r2h
V  3.14  1.52  12
V  cm3
Cylinder 2:
V = r2h
V  3.14  32  6
V  cm3
Cylinder 2 has the greater volume because
cm3 > cm3.

10. Find which cylinder has the greater volume.
Course 1
10-8
Volume of Cylinders
Check It Out: Example 3
Find which cylinder has the greater volume.
Cylinder 1:
V = r2h
10 cm
2.5 cm
4 cm
V  3.14  2.52  10
V  cm3
Cylinder 2:
V = r2h
V  3.14  22  4
V  cm3
Cylinder 1 has the greater volume because
cm3 > cm3.

11. Insert Lesson Title Here
Course 1
10-8
Volume of Cylinders
Insert Lesson Title Here
Lesson Quiz: Part I
Find the volume of each cylinder to the nearest cubic unit. Use 3.14 for .
1. radius = 9 ft, height = 4 ft
1,017 ft3
2. radius = 3.2 ft, height = 6 ft
193 ft3
3. Which cylinder has a greater volume?
a. radius 5.6 ft and height 12 ft
b. radius 9.1 ft and height 6 ft
cylinder b
1, ft3
1, ft3

12. Insert Lesson Title Here
Course 1
10-8
Volume of Cylinders
Insert Lesson Title Here
Lesson Quiz: Part II
4. Jeff’s drum kit has two small drums. The first drum has a radius of 3 in. and a height of 14 in. The other drum has a radius of 4 in. and a height of 12 in. Estimate the volume of each cylinder to the nearest cubic inch.
a. First drum
b. Second drum
about 396 in2
about 603 in2