Marcus is making spherical soaps to sell in his online store. The surface area of a soap is 63.585 inches squared and he wants to package them into a cube box so that it fits snugly. Using 3.14 as pi what should the dimensions of the cube box

Question

Marcus is making spherical soaps to sell in his online store. The surface area of a soap is 63.585 inches squared and he wants to package them into a cube box so that it fits snugly. Using 3.14 as pi what should the dimensions of the cube box

Answer 1

We can start by finding the radius of the sphere. The surface area of a sphere is given by the formula:

Surface Area = 4πr^2

Let's solve the equation for the radius (r):

63.585 = 4 * 3.14 * r^2
63.585 = 12.56 * r^2

Now, divide both sides by 12.56:

63.585 / 12.56 = r^2
5.07 = r^2

To find the radius, we take the square root of both sides:

√5.07 = r
2.25 ≈ r

Now that we have the radius, we can find the diameter by multiplying it by 2:

d = 2 * r
d = 2 * 2.25
d ≈ 4.5 inches

Since the diameter of the sphere equals the side length of the cube box, the dimensions of the cube box should be approximately 4.5 inches on each side.