1. Volume of Sectors of Cylinders Lesson 19

2. Find the area of the sectors labels at 1. Use 3.14 for π. Round to the nearest hundredth. 1. 2. 1 1

3. Target: Calculate the volume of sectors of cylinders.

5. 1. Find the volume of the cylinder. 2. Write a proportion. Set the ratio of the central angle to 360 ⁰ equal to the ratio of the volume of the sector to the volume of the cylinder. 3. Set the cross products equal to one another. Solve.

6. A cylinder has a radius of 5 cm and is 3 cm tall. Find the volume of a 90° slice of the cylinder. Use 3.14 for π.  Use the cylinder volume formula.V = πr 2 h  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 cm 3.

7. Taye made a cylindrical quiche to serve at brunch. The quiche was cut into equal-sized slices, each with a central angle of 45 ⁰. The volume of each slice was 12.5 cubic inches. 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 in 3.

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

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