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?

Answer 1

The surface area of a sphere can be calculated using the formula:

Surface Area = 4πr^2, where r is the radius of the sphere.

Given that the surface area of the soap is 63.585 in^2, we can set up the equation:

4πr^2 = 63.585

Simplifying the equation, we have:

r^2 = 63.585 / (4π)
r^2 = 63.585 / (4 * 3.14)
r^2 = 5.0684
r ≈ √5.0684
r ≈ 2.25

So, the radius of the sphere is approximately 2.25 inches.

To fit the spherical soaps into a cube box, the length, width, and height of the box should be equal to the diameter of the sphere, which is twice the radius.

Diameter = 2 * r
Diameter ≈ 2 * 2.25
Diameter ≈ 4.5 inches

Therefore, the dimensions of the cube box should be approximately 4.5 inches by 4.5 inches by 4.5 inches.