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 2.25 in. × 2.25 in. × 2.25 in. 2.25 inches times 2.25 inches times 2.25 inches 4.5 in. × 4.5 in. × 4.5 in. 4.5 inches times 4.5 inches times 4.5 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. 4 inches times 4 inches times 4 inches
Let r be the radius of the spherical soap. The surface area of the soap is given by the formula 4πr^2. We can set this equal to 63.585 and solve for r:
4πr^2 = 63.585
r^2 = 63.585 / (4π)
r^2 ≈ 5.038
r ≈ √5.038
r ≈ 2.242
Since the soap is spherical and we want it to fit snugly in a cube box, the side length of the cube box should be equal to the diameter of the soap, which is twice the radius:
Side length = 2 * 2.242
Side length ≈ 4.484
Therefore, the dimensions of the cube box should be approximately 4.484 inches × 4.484 inches × 4.484 inches. The closest option to this is 4 in. × 4 in. × 4 in.