Marcus is making spherical soaps to sell in his online store. The service area of a soap is 63.585 in.^2 and he wants to package them into a cube box so that it fits snuggly. Using 3.14 as the value of pi, what should be the dimensions of the cube box?
a. 4 in. x 4 in. x 4 in.
b. 2.25 in. x 2.25 in. x 2.25 in.
c. 4.5 in. x 4.5 in x 4.5 in.
d. 1.2 in. x 1.2 in. x 1.2 in.
To find the dimensions of the cube box that can snugly fit the spherical soap with a surface area of 63.585 in.^2, we first need to find the radius of the sphere.
The formula for the surface area of a sphere is A = 4πr^2.
Given that the surface area of the soap is 63.585 in.^2, we can set up the equation:
63.585 = 4 * 3.14 * r^2
r^2 = 63.585 / (4 * 3.14)
r^2 = 5.0838
r = √5.0838
r ≈ 2.25 in.
So, the radius of the sphere is approximately 2.25 in.
Since the cube needs to snugly fit the soap, each side of the cube should be equal to the diameter of the sphere, which is 2 * 2.25 = 4.5 in.
Therefore, the correct answer is:
c. 4.5 in. x 4.5 in. x 4.5 in.