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

Answer 1

To find the dimensions of the cube box, we need to find the side length of the cube since all sides are equal.
The surface area of a sphere is given by the formula:
Surface Area = 4πr^2
63.585 in.² = 4πr^2
r^2 = 63.585 in.² / (4π)
r^2 ≈ 5.065 in.² / (π)
r^2 ≈ 1.614 in.²
r ≈ √(1.614 in.²)
r ≈ 1.27 in.

The side length of the cube will be equal to the diameter of the sphere.

Diameter = 2r
Diameter ≈ 2 * 1.27 in.
Diameter ≈ 2.54 in.

Therefore, the dimensions of the cube box should be approximately 2.54 inches on each side.