Marcus is making spherical soaps to sell in his online store. The surface area of a soap is 63.585 in.2 and he wants to package them into a cube box so that it fits snugly. Using 3.14 as the value of pi, what should be the dimensions of the cube box?(1 point)
Responses
4.5 in. × 4.5 in. × 4.5 in.
4.5 inches times 4.5 inches times 4.5 inches
2.25 in. × 2.25 in. × 2.25 in.
2.25 inches times 2.25 inches times 2.25 inches
1.2 in. × 1.2 in. × 1.2 in.
1.2 inches times 1.2 inches times 1.2 inches
4 in.× 4 in.× 4 in.
To find the dimensions of the cube box, we need to find the length of each side of the cube. Since the surface area of a sphere is given by the formula 4πr^2, where r is the radius of the sphere, we can solve for the radius using the given surface area:
4πr^2 = 63.585
r^2 = 63.585 / (4π)
r^2 = 63.585 / (4 * 3.14)
r^2 ≈ 5.07
Taking the square root of both sides, we find:
r ≈ √5.07
r ≈ 2.25
Therefore, the radius of the sphere is approximately 2.25 inches. Since a cube has all sides equal, the dimensions of the cube box should be:
2.25 inches times 2.25 inches times 2.25 inches.
Therefore, the correct answer is 2.25 in. × 2.25 in. × 2.25 in.