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
2.25 in. × 2.25 in. × 2.25 in.
2.25 inches times 2.25 inches times 2.25 inches
4.5 in. × 4.5 in. × 4.5 in.
4.5 inches times 4.5 inches times 4.5 inches
4 in.× 4 in.× 4 in.
4 inches times 4 inches times 4 inches
1.2 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, we need to calculate the volume of the soap and then use that value to find the dimensions of the cube.
The surface area of a sphere is given by the formula:
Surface Area = 4πr^2
Given that the surface area of the soap is 63.585 in.2, we can set up the equation as:
63.585 = 4πr^2
To solve for the radius, we divide both sides by 4π:
r^2 = 63.585 / (4π)
r^2 = 5.0625
Taking the square root of both sides, we find:
r ≈ 2.25
Now that we have the radius, we can calculate the volume of the soap using the formula:
Volume = (4/3)πr^3
Volume = (4/3)π(2.25)^3
Volume ≈ 38.016 in.3
Since a cube has all sides equal, we can find the length of one side by taking the cube root of the volume:
Side Length = ∛(Volume)
Side Length ≈ ∛(38.016)
Side Length ≈ 3.355
Therefore, the dimensions of the cube box should be approximately 3.355 in. × 3.355 in. × 3.355 in.