Question

Sophie has a hard rubber ball whose circumference measures 13 inches. she wants to store it in a box. what is the number of cubic inches in the volume of the smallest cube- shaped box with integer dimensions that she can use?

Answer 1

Let r = radius of the hard rubber ball.
The circumference of the ball is 13 inches, therefore
2πr = 13
r = 13/(2π) = 2.069 inches
The diameter of the ball is 2*2.069 = 4.138 inches.

The ball is hard and cannot be compressed. Therefore the length of a side of the smallest cube-shaped box with integer dimensions is 5 inches.
The volume of the box is 5³ = 125 in³.

Answer: 125 in³