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?
The surface area of a sphere is given by the formula:
Surface Area = 4πr^2
Given that the surface area of the soap is 63.585 in^2, we can set up the equation as follows:
4πr^2 = 63.585
Now, let's solve for the radius (r):
r^2 = 63.585 / (4π)
r^2 = 63.585 / (4*3.14)
r^2 ≈ 5.072
Taking the square root of both sides, we find:
r ≈ √5.072
r ≈ 2.25
The diameter of the sphere is twice the radius, so:
d ≈ 2 * 2.25
d ≈ 4.50
Now we can find the dimensions of the cube box. Since the sphere should fit snugly inside the cube, the length, width, and height of the cube should be equal to the diameter of the sphere.
Therefore, the dimensions of the cube box should be approximately 4.50 inches in length, width, and height.