A ball will fit inside a cubed box. The surface area of the ball is 1017.36 square inches. The box has 6 sides. What is the side length of the box?
To find the side length of the box, we first need to find the diameter of the ball.
The surface area of a sphere is given by the formula:
Surface Area = 4πr^2
where r is the radius of the sphere.
Given that the surface area of the ball is 1017.36 square inches, we can set up the equation:
4πr^2 = 1017.36
r^2 = 1017.36 / 4π
r^2 ≈ 81.18
r ≈ √81.18
r ≈ 9 inches
So, the diameter of the ball is 18 inches.
Since the ball can fit inside the box, the side length of the box must be greater than or equal to the diameter of the ball.
Therefore, the side length of the box is 18 inches.