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
1.2 in. × 1.2 in. × 1.2 in.
1.2 inches times 1.2 inches times 1.2 inches
4 in.× 4 in.× 4 in.
4 inches times 4 inches times 4 inches
4.5 in. × 4.5 in. × 4.5 in.
4.5 inches times 4.5 inches times 4.5 inches
2.25 in. × 2.25 in. × 2.25 in.
2.25 inches times 2.25 inches times 2.25 inches
To find the dimensions of the cube box, we need to determine the side length of the cube.
The formula for the surface area of a sphere is A = 4πr^2, where A is the surface area and r is the radius.
In this case, the surface area of the soap is given as 63.585 in^2. We can set up the equation as follows:
63.585 = 4πr^2
To solve for r, we divide both sides of the equation by 4π:
r^2 = 63.585 / (4π)
r^2 = 5.067
r = √5.067
r ≈ 2.249
Since the cube box will fit snugly around the soap, the side length of the cube should be equal to twice the radius. Therefore, the side length of the cube should be approximately:
2 × 2.249 = 4.498 ≈ 4.5 inches
Therefore, the dimensions of the cube box should be 4.5 in. × 4.5 in. × 4.5 in.