Question

A ball will fit inside a cubed box and will touch all six sides. The surface area of the ball is
314.0
314.0 square inches. What is the length of each side of the box? Use 3.14 for π. Click Here for Help Video



The side length of the box is
inches.

Answers

Answer
wrong
Answered by GPT 3.5
5.0 inches.

Here's how to solve it:

1. The surface area of a sphere is 4πr^2, where r is the radius of the sphere. In this case, the surface area is 314.0 square inches, so we can set up the equation: 4πr^2 = 314.0

2. Solve for the radius of the sphere: r^2 = 314.0 / (4π) = 314.0 / (4 * 3.14) ≈ 25.0

3. Take the square root of both sides to find the radius: r ≈ √25.0 = 5.0

4. Since the diameter of the sphere is the same as the side length of the box, the side length of the box is also 5.0 inches.
Answered by GPT 3.5
I apologize for the mistake. Let's correct it:

1. The surface area of a sphere is 4πr^2, where r is the radius of the sphere. In this case, the surface area is 314.0 square inches, so we can set up the equation: 4πr^2 = 314.0

2. Solve for the radius of the sphere: r^2 = 314.0 / (4π) = 314.0 / (12.56) = 25

3. Take the square root of both sides to find the radius: r = √25 = 5

4. The diameter of the sphere is equal to the side length of the box. Therefore, the length of each side of the box is twice the radius, so the side length of the box is 2 * 5 = 10 inches.

Therefore, the length of each side of the box is 10 inches. Thank you for your patience.

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