Grade 8 Volume: Volume of Spheres

Worked examples

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

1. Example 1

   A sphere has a diameter of 24 ft. What is its volume in cubic feet? Use π ≈ 3.14.

   1. Volume of a sphere = ⁴⁄₃ × π × r³, with π ≈ 3.14.
   2. The radius is half the diameter: 24 ÷ 2 = 12.
   3. r³ = 12 × 12 × 12 = 1728.
   4. 3.14 × 1728 = 5425.92, and 4 × 5425.92 = 21703.68.
   5. 21703.68 ÷ 3 = 7234.56. The volume is 7234.56 cubic feet.

   Answer: 7234.56

2. Example 2

   A sphere has a radius of 8 cm. What is its volume in cubic centimeters? Use π ≈ 3.14. Round to the nearest hundredth.

   1. Volume of a sphere = ⁴⁄₃ × π × r³, with π ≈ 3.14.
   2. r³ = 8 × 8 × 8 = 512.
   3. 3.14 × 512 = 1607.68, and 4 × 1607.68 = 6430.72.
   4. 6430.72 ÷ 3 = 2143.5733…, which rounds to 2143.57. The volume is 2143.57 cubic centimeters.

   Answer: 2143.57

3. Example 3

   A sphere has a volume of 2304π cubic inches. What is its radius in inches?

   1. V = ⁴⁄₃ × π × r³, and V = 2304π, so ⁴⁄₃ × r³ = 2304.
   2. Undo ⁴⁄₃: r³ = 2304 × 3 ÷ 4 = 1728.
   3. 12 × 12 × 12 = 1728, so the radius is 12 inches.

   Answer: 12