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
1.2 in. × 1.2 in. × 1.2 in.
1.2 inches times 1.2 inches times 1.2 inches
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
4 in.× 4 in.× 4 in.
1.2 in. × 1.2 in. × 1.2 in.
To find the dimensions of the cube box that will fit the spherical soaps snugly, we need to find the edge length of the cube. The formula for the surface area of a sphere is 4πr^2, where r is the radius of the sphere. So, the radius of the sphere is √(63.585 / 4π) ≈ 2.017 inches.
To fit the sphere snugly, the side length of the cube should be equal to the diameter of the sphere. So, the side length of the cube should be twice the radius, which is 2 × 2.017 ≈ 4.034 inches. Since the answer choices are in whole numbers, we round this value down to get 4 inches.
Therefore, the correct answer is 4 in.× 4 in.× 4 in.