A ball will fit inside a cube box and will touch all six sides. The surface area of the ball is 1017.36 square inches. What is the length of each side of the box. Used 3.14 for pie
To find the surface area of the ball, we use the formula:
Surface area of a sphere = 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:
4 * 3.14 * r^2 = 1017.36
Solving for r:
r^2 = 1017.36 / (4 * 3.14)
r^2 = 81.25
r = √81.25
r = 9
Now we know the radius of the ball is 9 inches.
Since the ball touches all six sides of the cube box, the diameter of the ball is equal to the length of the side of the box.
Therefore, the length of each side of the cube box is 9 * 2 = 18 inches.