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?
To find the dimensions of the cube box, we need to determine the side length of the cube.
The surface area of a sphere is given by the formula A = 4πr^2, where A is the surface area and r is the radius.
Given that the surface area of the soap is 63.585 in^2, we have:
63.585 = 4πr^2.
Dividing both sides by 4π, we get:
r^2 = 63.585 / (4π).
Using 3.14 as the value of pi, we can calculate:
r^2 = 63.585 / (4 * 3.14) ≈ 5.0834.
Taking the square root of both sides, we find:
r ≈ √5.0834 ≈ 2.25.
Now that we have the radius, we know that the diameter of the sphere is twice the radius, or 2 * 2.25 = 4.5 inches.
Since the cube box needs to fit the sphere snugly, the side length of the cube box should be equal to the diameter of the sphere, or 4.5 inches.
Therefore, the dimensions of the cube box should be 4.5 inches on each side.