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)
To find the dimensions of the cube box, we first need to determine the side length of the cube.
The surface area of a sphere is given by the formula: A = 4πr^2
Given that the surface area of the soap is 63.585 in^2, we can set up the equation:
63.585 = 4πr^2
Next, we can solve for r:
63.585 = 4(3.14)r^2
Dividing both sides by 4(3.14), we get:
r^2 = 63.585 / (4(3.14))
r^2 ≈ 5.0707
Taking the square root of both sides, we find:
r ≈ √(5.0707)
r ≈ 2.25
Now, we know that the side length of the cube box must be equal to the diameter of the soap, which is twice the radius.
Therefore, the dimensions of the cube box should be approximately 2.25 in x 2.25 in x 2.25 in.