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
To find the length of each side of the box, we need to first find the radius of the ball.
The surface area of a sphere is calculated by the formula: 4πr^2, where r is the radius.
Given that the surface area of the ball is 1017.36 square inches, we can set up the following equation:
4 * 3.14 * r^2 = 1017.36
12.56 * r^2 = 1017.36
r^2 = 1017.36 / 12.56
r^2 = 81
Therefore, the radius of the ball is √81 = 9 inches.
Since the ball touches all 6 sides of the cubed box, the diameter of the ball would be equal to the length of the side of the box.
Therefore, the length of each side of the box is 18 inches.