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10-8
Volume of Cylinders Notes
Course 1
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.
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.
Write the formula.
Replace with 3.14, r with 4, and h with 7.Multiply.V 351.68
V = r2h
V 3.14 42 7
The volume is about 352 ft3.
Course 1
10-8 Volume of Cylinders
Additional Example 1B: Finding the Volume of a Cylinder
10 cm ÷ 2 = 5 cm Find the radius.
Write the formula.
Replace with 3.14, r with 5, and h with 11.Multiply.V 863.5
V = r2h
V 3.14 52 11
The volume is about 864 cm3.
Course 1
10-8 Volume of Cylinders
Additional Example 1C: Finding the Volume of a Cylinder
Find the radius.r = + 4h3__
r = + 4 = 793__ Substitute 9 for h.
Write the formula.
Replace with 3.14, r with 7, and h with 9.Multiply.V 1,384.74
V = r2h
V 3.14 72 9
The volume is about 1,385 in3.Course 1
10-8 Volume of Cylinders
Check It Out: Example 1A
Find the volume V of each cylinder to the nearest cubic unit.
Multiply.V 565.2
The volume is about 565 ft3.
6 ft
5 ft
Write the formula.
Replace with 3.14, r with 6, and h with 5.
V = r2h
V 3.14 62 5
Course 1
10-8 Volume of Cylinders
Check It Out: Example 1B
Multiply.V 301.44
8 cm ÷ 2 = 4 cm
The volume is about 301 cm3.
Find the radius.
8 cm
6 cm
Write the formula.
Replace with 3.14, r with 4, and h with 16.
V = r2h
V 3.14 42 6
Course 1
10-8 Volume of Cylinders
Check It Out: Example 1C
Multiply.V 1230.88
The volume is about 1,231 in3.
Find the radius.r = + 5h4__
r = + 5 = 784__ Substitute 8 for h.
r = + 5
h = 8 in
h4
Write the formula.
Replace with 3.14, r with 7, and h with 8.
V = r2h
V 3.14 72 8
Course 1
10-8 Volume of Cylinders
Additional Example 3: Comparing Volumes of Cylinders
Find which cylinder has the greater volume.
Cylinder 1:
V 3.14 1.52 12V = r2h
V 84.78 cm3
Cylinder 2:
V 3.14 32 6V = r2h
V 169.56 cm3
Cylinder 2 has the greater volume because 169.56 cm3 > 84.78 cm3.
Course 1
10-8 Volume of Cylinders
Check It Out: Example 3
Find which cylinder has the greater volume.
Cylinder 1:
V 3.14 2.52 10V = r2h
V 196.25 cm3
Cylinder 2:
V 3.14 22 4V = r2h
V 50.24 cm3
Cylinder 1 has the greater volume because 196.25 cm3 > 50.24 cm3.
Course 1
10-8 Volume of Cylinders
10 cm2.5 cm
4 cm
4 cm
Lesson Quiz: Part I
Find the volume of each cylinder to the nearest cubic unit. Use 3.14 for .
Insert Lesson Title Here
cylinder b
1,560.14 ft3
193 ft3
1,017 ft3
1,181.64 ft3
Course 1
10-8 Volume of Cylinders
1. radius = 9 ft, height = 4 ft
2. radius = 3.2 ft, height = 6 ft
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
Lesson Quiz: Part II
Insert Lesson Title Here
about 396 in2
Course 1
10-8 Volume of Cylinders
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 603 in2
