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?

Question

4 in.× 4 in.× 4 in.4 inches times 4 inches times 4 inches4.5 in. × 4.5 in. × 4.5 in.4.5 inches times 4.5 inches times 4.5 inches2.25 in. × 2.25 in. × 2.25 in.2.25 inches times 2.25 inches times 2.25 inches1.2 in. × 1.2 in. × 1.2 in.1.2 inches times 1.2 inches times 1.2 inches

Answer 1

To find the dimensions of the cube box that will fit the spherical soaps, we need to find the diameter of the sphere.

The formula for the surface area of a sphere is given by:
Surface Area = 4πr^2

We are given that the surface area of the soap is 63.585 in^2. So we can set up the equation:
63.585 = 4πr^2

Simplifying the equation:
63.585 = 4(3.14)(r^2)
63.585 = 12.56r^2
r^2 = 63.585/12.56
r^2 = 5.068

Taking the square root of both sides to find the radius:
r = √(5.068)
r ≈ 2.25 inches

Now, the diameter of the sphere is 2r which is approximately 2(2.25) = 4.5 inches.

Since a cube has equal sides, the dimensions of the cube box should be 4.5 inches × 4.5 inches × 4.5 inches.
Therefore, the correct answer is 4.5 in. × 4.5 in. × 4.5 in.