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?
4 in.× 4 in.× 4 in.4 inches times 4 inches times 4 inches4.5 in. × 4.5 in. × 4.5 in.4.5 inches times 4.5 inches times 4.5 inches2.25 in. × 2.25 in. × 2.25 in.2.25 inches times 2.25 inches times 2.25 inches1.2 in. × 1.2 in. × 1.2 in.1.2 inches times 1.2 inches times 1.2 inches
To find the dimensions of the cube box that will fit the spherical soaps, we need to find the diameter of the sphere.
The formula for the surface area of a sphere is given by:
Surface Area = 4πr^2
We are given that the surface area of the soap is 63.585 in^2. So we can set up the equation:
63.585 = 4πr^2
Simplifying the equation:
63.585 = 4(3.14)(r^2)
63.585 = 12.56r^2
r^2 = 63.585/12.56
r^2 = 5.068
Taking the square root of both sides to find the radius:
r = √(5.068)
r ≈ 2.25 inches
Now, the diameter of the sphere is 2r which is approximately 2(2.25) = 4.5 inches.
Since a cube has equal sides, the dimensions of the cube box should be 4.5 inches × 4.5 inches × 4.5 inches.
Therefore, the correct answer is 4.5 in. × 4.5 in. × 4.5 in.