A hollow ball is made of rubber that is 2 cm thick. The ball has a radius to the outside surface of 6 cm.

What is the approximate volume of rubber used to make the ball?

Use 3.14 to approximate pi.

A. 33.5 cm³

B. 267.9 cm³

C. 636.4 cm³

D. 904.3 cm³

The answer is C. 636.4 cm³

Step 1. Calculate the volume of the ball with radius to the outside surface (V1 = ?).

Step 2. Calculate the volume of the ball with radius to the inside surface (V2 = ?).

Step 3. Find a difference between two volumes (V1 - V2) which is actually the approximate volume of rubber used to make the ball (V = ?)

The volume of the sphere with radius r is:

V = 4/3 * π * r³

Step 1. V1 = ?

V1 = 4/3 * π * r1³

r1 = 6 cm

π = 3.14

V1 = 4/3 * 3.14 * 6³

V1 = 4/3 * 3.14 * 216

V1 = 904.32 cm³

Step 2. V2 = ?

V2 = 4/3 * π * r2³

The radius to the inside surface is actually a difference between the radius to the outside surface (6 cm) and the thickness of the rubber (2 cm).

r2 = 6 cm - 2 cm = 4 cm

π = 3.14

V2 = 4/3 * 3.14 * 4³

V2 = 4/3 * 3.14 * 64

V2 = 267.95 cm³

Step 3. The volume of the rubber (V) is:

V = V1 - V2 = 904.32 cm³ - 267.95 cm³ = 636.37 cm³ ≈ 636.4 cm³