Marcus is making spherical soaps to sell in his online store the service area of a soap is 63.585 inches ^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 determine the side length of the cube.
The surface area of a cube is given by the formula: A = 6s^2, where A is the surface area and s is the side length.
In this case, we want to find the side length of the cube box that will accommodate the spherical soap. Since the soap's service area is 63.585 inches^2, this should be equal to the surface area of the cube, which is 6s^2.
So, we have: 6s^2 = 63.585.
Dividing both sides of the equation by 6: s^2 = 10.5975.
To isolate s, take the square root of both sides: s ≈ √10.5975.
Using a calculator, we find that s ≈ 3.25 inches (rounded to two decimal places).
Therefore, the approximate dimensions of the cube box should be 3.25 inches on each side.