Grade 8 Volume: Unit Review

Worked examples

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

1. Example 1

   A sphere has a volume of 562.5π cubic inches. What is its radius in inches?

   1. V = ⁴⁄₃ × π × r³, and V = 562.5π, so ⁴⁄₃ × r³ = 562.5.
   2. Undo ⁴⁄₃: r³ = 562.5 × 3 ÷ 4 = 421.875.
   3. 7.5 × 7.5 × 7.5 = 421.875, so the radius is 7.5 inches.

   Answer: 7.5

2. Example 2

   A cylinder and a cone both have radius 8 m and height 3 m. The cylinder's volume is 602.88 cubic meters. What is the cone's volume in cubic meters?

   1. A cone holds exactly ⅓ of a cylinder with the same radius and height.
   2. 602.88 ÷ 3 = 200.96.
   3. The cone’s volume is 200.96 cubic meters.

   Answer: 200.96

3. Example 3

   A rocket model is a cylinder with a cone on top. Both have radius 7 in. The cylinder is 10 in tall and the cone is 6 in tall. What is the total volume in cubic inches? Use π ≈ 3.14.

   1. Find each part, then add.
   2. Cylinder: π × r² × h = 3.14 × 49 × 10 = 3.14 × 490 = 1538.6.
   3. Cone: ⅓ × π × r² × h = 3.14 × (294 ÷ 3) = 3.14 × 98 = 307.72.
   4. 1538.6 + 307.72 = 1846.32. The volume is 1846.32 cubic inches.

   Answer: 1846.32