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
To find the length of each side of the box, we first need to find the radius of the ball.
The surface area of a sphere is given by the formula:
A = 4πr^2
Given that the surface area of the ball is 1017.36 square inches, we can plug this into the formula:
1017.36 = 4 * 3.14 * r^2
Solving for r:
r^2 = 1017.36 / (4 * 3.14)
r^2 = 81.25
r = √81.25
r = 9
Now that we have found the radius of the ball, we know that the diameter of the ball is twice the radius, so the diameter is 18 inches.
Since the ball will touch all 6 sides of the cubed box, the diameter of the ball will be equal to the length of the side of the box.
Therefore, each side of the box is 18 inches long.