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?

Let r = radius of the hard rubber ball.

Because the circumference of the ball is 13 inches, therefore

2πr = 13

r = 13 / (2π) = 2.069 in

In order to fit the ball into a cube-shaped box with integer dimensions, each side of the box should measure 3 inches (the next integer greater than 2.069).

The volume of the cube-shaped box is 3³ = 27 in³.

Answer: The volume is 27 in³.