Marcus is making spherical soaps to sell in his online store. The surface area of a soap is 63.585 in squared 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?
4 in * 4 in * 4 in
1.2 in * 1.2 in * 1.2 in
4.5 in * 4.5 in * 4.5 in
2.25 in * 2.25 in * 2.25 in
To find the dimensions of the cube box that can snugly fit the soap, we first need to find the diameter of the spherical soap to determine the size of the smallest cube that can enclose it.
The formula to find the surface area (A) of a sphere is:
A = 4 * pi * r^2
We're given the surface area A = 63.585 square inches and pi = 3.14. Let's solve for the radius (r):
63.585 = 4 * 3.14 * r^2
63.585 = 12.56 * r^2
Now, divide both sides by 12.56 to solve for r^2:
r^2 = 63.585 / 12.56
r^2 ≈ 5.0648
Now, take the square root of both sides to find r:
r ≈ sqrt(5.0648)
r ≈ 2.25 inches
The diameter (d) of the sphere is twice the radius:
d = 2 * r
d = 2 * 2.25 inches
d = 4.5 inches
The cube box needs to have internal dimensions that are at least the diameter of the sphere to fit snugly. Therefore, the cube box should have dimensions of:
4.5 in * 4.5 in * 4.5 in
Among the options given, the correct answer is:
4.5 in * 4.5 in * 4.5 in