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)
To find the dimensions of the cube box that will snugly fit the spherical soaps, we need to determine the side length of the cube.
First, let's find the radius of the spherical soap.
The formula for the surface area of a sphere is given by:
Surface Area = 4πr^2
Here, the surface area of the soap is given as 63.585 in.².
63.585 = 4 * 3.14 * r^2
Dividing both sides by 4 * 3.14:
(63.585) / (4 * 3.14) = r^2
r^2 ≈ 5.07
Taking the square root of both sides, we find:
r ≈ √(5.07) ≈ 2.25
So, the radius of the spherical soap is approximately 2.25 in.
Since the soap needs to fit snugly inside the cube, the side length of the cube should be equal to the diameter of the sphere, which is twice the radius.
Side length of cube = 2 * r ≈ 2 * 2.25 = 4.5
Therefore, the dimensions of the cube box should be approximately 4.5 inches on each side.