Grade 8 Volume: Volume of Cones

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   A cone has diameter 12 ft and height 10 ft. What is its volume in cubic feet? Use π ≈ 3.14.

   1. Volume of a cone = ⅓ × π × r² × h, with π ≈ 3.14.
   2. The radius is half the diameter: 12 ÷ 2 = 6.
   3. r² × h = 6 × 6 × 10 = 360.
   4. Take a third: 360 ÷ 3 = 120.
   5. 3.14 × 120 = 376.8. The volume is 376.8 cubic feet.

   Answer: 376.8

2. Example 2

   A cylinder and a cone both have radius 3 in and height 9 in. The cylinder's volume is 254.34 cubic inches. What is the cone's volume in cubic inches?

   1. A cone holds exactly ⅓ of a cylinder with the same radius and height.
   2. 254.34 ÷ 3 = 84.78.
   3. The cone’s volume is 84.78 cubic inches.

   Answer: 84.78

3. Example 3

   A cone has a volume of 153.86 cubic centimeters and a radius of 7 cm. What is its height in centimeters? Use π ≈ 3.14.

   1. V = ⅓ × π × r² × h, so h = 3 × V ÷ (π × r²).
   2. 3 × 153.86 = 461.58.
   3. π × r² = 3.14 × 49 = 153.86.
   4. 461.58 ÷ 153.86 = 3. The height is 3 centimeters.

   Answer: 3