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?
To find the dimensions of the cube box, we need to find the side length of the cube.
Let's assume the side length of the cube box is s.
The surface area of a cube is given by the formula: surface area = 6s^2.
We want the surface area of the cube box to be equal to the surface area of the soap, which is 63.585 in.^2.
Setting up the equation: 6s^2 = 63.585.
Divide both sides by 6: s^2 = 63.585 / 6.
Simplify: s^2 = 10.5975.
Take the square root of both sides: s = √10.5975.
Using a calculator, s ≈ 3.256 in.
Therefore, the side length of the cube box should be approximately 3.256 inches.