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) Responses
To find the dimensions of the cube box, we need to find the side length of the cube since all sides are equal.
The surface area of a sphere is given by the formula:
Surface Area = 4πr^2
63.585 in.² = 4πr^2
r^2 = 63.585 in.² / (4π)
r^2 ≈ 5.065 in.² / (π)
r^2 ≈ 1.614 in.²
r ≈ √(1.614 in.²)
r ≈ 1.27 in.
The side length of the cube will be equal to the diameter of the sphere.
Diameter = 2r
Diameter ≈ 2 * 1.27 in.
Diameter ≈ 2.54 in.
Therefore, the dimensions of the cube box should be approximately 2.54 inches on each side.