Holt CA Course 1

10-9 Volume of Cylinders

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Holt CA Course 1

10-9 Volume of Cylinders

Warm UpFind the volume of each figure described.

359.04 cm3

1,320 cm3

1. rectangular prism with length 12 cm, width 11 cm, and height 10 cm

2. triangular prism with height 11 cm and triangular base with base length 10.2 cm and height 6.4 cm

Holt CA Course 1

10-9 Volume of Cylinders

MG1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid.Also covered: AF3.1, AF3.2

California Standards

Holt CA Course 1

10-9 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.

V = Bh

The area of the circular base is r2.

V = r2h

Holt CA Course 1

10-9 Volume of CylindersAdditional Example 1A: Finding the Volume of a

CylinderFind 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 = r2hV 3.14 42 7

The volume is about 352 ft3.

Holt CA Course 1

10-9 Volume of Cylinders Additional Example 2A: Application Ali has a cylinder-shaped pencil holder with a 3 in. diameter and a height of 5 in. Scott has a cylinder-shaped pencil holder with a 4 in. diameter and a height of 6 in. Estimate the volume of each cylinder to the nearest cubic inch.Ali’s pencil holder

Write the formula.Replace with 3.14, r with 1.5, and h with 5.Multiply.V 35.325

3 in. ÷ 2 = 1.5 in.

V 3.14 1.52 5

The volume of Ali’s pencil holder is about 35 in3.

Find the radius.

V = r2h

Holt CA Course 1

10-9 Volume of CylindersAdditional 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.

Holt CA Course 1

10-9 Volume of CylindersCheck It Out! Example 1A

Find the volume V of the cylinder to the nearest cubic unit.

Multiply.V 565.2The volume is about 565 ft3.

6 ft

5 ft

Write the formula.Replace with 3.14, r with 6, and h with 5.

V = r2hV 3.14 62 5

Holt CA Course 1

10-9 Volume of CylindersCheck It Out! Example 2A

Sara has a cylinder-shaped sunglasses case with a 3 in. diameter and a height of 6 in. Ulysses has a cylinder-shaped pencil holder with a 4 in. diameter and a height of 7 in. Estimate the volume of each cylinder to the nearest cubic inch.Sara’s sunglasses case

Write the formula.Replace with 3.14, r with 1.5, and h with 6.Multiply.V 42.39

3 in. ÷ 2 = 1.5 in.

V 3.14 1.52 6

The volume of Sara’s sunglasses case is about 42 in3.

Find the radius.V = r2h

Holt CA Course 1

10-9 Volume of CylindersCheck 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.

10 cm2.5 cm

4 cm

4 cm

Holt CA Course 1

10-9 Volume of CylindersLesson Quiz: Part I

Find the volume of each cylinder to the nearest cubic unit. Use 3.14 as an estimate for .

cylinder b≈ 1,560.14 ft3

193 ft3

1,017 ft3

≈1,181.64 ft3

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

Holt CA Course 1

10-9 Volume of CylindersLesson Quiz: Part II

about 396 in2

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 drumb. Second drum about 603 in2