Question

A ball will fit inside a cubed box and will touch all 6 sides. The surface area of the ball is 1017.36 square inches. What is the length of each side of the box. Use 3.14 for pi

Answer 1

The surface area of a sphere is given by the formula $4\pi r^2$, where $r$ is the radius of the sphere. Since the surface area of the ball is 1017.36 square inches, we can set up the following equation:

$4\pi r^2 = 1017.36$

$4(3.14)r^2 = 1017.36$

$12.56r^2 = 1017.36$

$r^2 = 81

$r = 9$

Since the ball touches all 6 sides of the cube, the diameter of the ball is equal to the length of the side of the cube. Therefore, the length of each side of the cube is 9 inches.