A ball will fit inside a cute box and will touch all six sides. The surface area of a ball is 1017.36 in.². What is the length of each side of the box. Use 3.14 as pi.
To find the length of each side of the box, we first need to find the diameter of the ball.
Given that the surface area of a sphere is calculated using the formula 4πr², we can set this equation equal to 1017.36 in.² and solve for the radius:
4πr² = 1017.36
r² = 1017.36 / (4 * 3.14)
r² = 80.96
r = √80.96
r = 9 in
Therefore, the diameter of the ball is 18 inches. Since the ball will touch all six sides of the box, its diameter should be equal to the diagonal of the box.
Using the formula for the diagonal of a rectangular box, diagonal² = l² + w² + h², where l, w, and h are the length, width, and height of the box, we can solve for the length of each side:
18² = l² + l² + l²
18² = 3l²
l = √(18² / 3)
l = 6√3
So, the length of each side of the box would be approximately 6√3 inches.