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.
First, we need to find the radius of the ball.
The surface area of a sphere is given by the formula: 4πr^2, where r is the radius of the sphere.
We know the surface area of the ball is 1017.36 square inches, so we can set up the equation:
4πr^2 = 1017.36
4 * 3.14 * r^2 = 1017.36
12.56r^2 = 1017.36
r^2 = 1017.36 / 12.56
r^2 = 80.9
r ≈ √80.9
r ≈ 9 inches
Since the ball will touch all 6 sides of the cube, the diameter of the ball is equal to the side length of the box. So the side length of the box is 2r:
side length = 2 * 9
side length = 18 inches
Therefore, the length of each side of the box is 18 inches.