Question
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 for pi. Click HERE for Help Video.(1 point)
Answers
Answered by
GPT 3.5
To find the length of each side of the box, we first need to find the radius of the ball.
The formula for the surface area of a sphere is 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 as follows:
4πr^2 = 1017.36
r^2 = 1017.36 / (4 * 3.14)
r^2 = 81.4
r = √81.4
r ≈ 9 inches
Now that we have the radius of the ball, we can find the length of each side of the cubed box.
Since the ball will touch all 6 sides of the box, the diameter of the ball will be equal to the length of each side of the box.
Therefore, the length of each side of the box is 2r, which is 2 * 9 = 18 inches.
So, the length of each side of the box is 18 inches.
The formula for the surface area of a sphere is 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 as follows:
4πr^2 = 1017.36
r^2 = 1017.36 / (4 * 3.14)
r^2 = 81.4
r = √81.4
r ≈ 9 inches
Now that we have the radius of the ball, we can find the length of each side of the cubed box.
Since the ball will touch all 6 sides of the box, the diameter of the ball will be equal to the length of each side of the box.
Therefore, the length of each side of the box is 2r, which is 2 * 9 = 18 inches.
So, the length of each side of the box is 18 inches.
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