To find the length of each side of the box, we first need to find the diameter of the ball, which is equal to the square root of the surface area of the ball divided by pi (since the surface area of a sphere is given by A = 4πr^2, where r is the radius).
Therefore, the diameter of the ball is:
d = sqrt(1017.36/pi) = sqrt(324) ≈ 18 inches
Since the ball touches all 6 sides of the box, the diagonal of the box is equal to the diameter of the ball. Using the Pythagorean theorem, we know that the diagonal of the box is found by:
d = sqrt(3*a^2)
Where a is the length of each side of the box. Therefore, we can solve for a:
18 = sqrt(3*a^2)
18^2 = 3*a^2
324 = 3*a^2
108 = a^2
a = sqrt(108) ≈ 10.39 inches
Therefore, the length of each side of the box is approximately 10.39 inches.
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.
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