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.
The side length of the box is inches.

Answer 1

The surface area of a sphere can be calculated using the formula:

Surface area = 4πr^2

Given that the surface area of the ball is 1017.36 square inches, we can set up the equation:

1017.36 = 4 * 3.14 * r^2

Solving for r, we get:

r^2 = 1017.36 / (4 * 3.14)
r^2 = 80.92
r = √80.92
r ≈ 9

Since the ball touches all 6 sides of the cube, the diameter of the ball (which is equal to twice the radius) must be equal to the length of each side of the cube. Therefore, the length of each side of the cube is approximately 18 inches.