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.