Volume of Sectors of Cylinders

Lesson 19

Find the area of the sectors labels at 1. Use 3.14 for π. Round to the nearest hundredth.

1.

2.

1

1

Target: Calculate the volume of sectors of cylinders.

1. Find the volume of the cylinder.

2. Write a proportion. Set the ratio of the central angle to 360 equal to the ratio of the volume of the sector ⁰to the volume of the cylinder.

3. Set the cross products equal to one another. Solve.

cylinder theof volume

sector theof volume

360

sector theof degree

A cylinder has a radius of 5 cm and is 3 cm tall. Find thevolume of a 90° slice of the cylinder. Use 3.14 for π.

Use the cylinder volume formula. V = πr2h Substitute all known values. V ≈ (3.14)(5)2(3) Evaluate. V ≈ 235.5 Write a proportion to find the volume of the sector. Set cross products equal. 360x ≈ 21,195 Divide by 360 on both sides. 360 360

x ≈ 58.875 The sector has a volume of about 58.875 cm3.

5.235360

90 x

Taye made a cylindrical quiche to serve at brunch. The quiche was cut into equal-sized slices, each with a centralangle of 45 . The volume of each slice was 12.5 cubic ⁰inches. What was the volume of the entire quiche?

Substitute known values into a proportion.

Set cross products equal. 45x = 4500 45 45

Divide. x = 100

The volume of the entire quiche was 100 in3.

x

5.12

360

45

Set up and write a proportion then find the volume of the sector. Use 3.14 for .

Describe how to find the volume of a sector of a cylinder.