Question

A ball is made of a plastic sphere covered with a layer of rubber. The plastic sphere has a radius of 18 in., and the ball itself has a radius of 22 in.
What is the volume of the rubber layer? Use 3.14 to approximate pi and round the answer to two decimal places.

___in3

Answer 1

Rl - rubber layer, s - sphere, b - ball

$V_{rl}=V_b-V_s\\ V=\dfrac{4}{3}\pi R^3\\\\\\ V_{rl}=\dfrac{4}{3}\cdot3.14\cdot22^3-\dfrac{4}{3}\cdot3.14\cdot18^3\\ V_{rl}=\dfrac{4}{3}\cdot3.14(10648-5832)\\ V_{rl}=\dfrac{4}{3}\cdot3.14\cdot4816\\ V_{rl}=20162.99\text { in}^3$