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
4.5 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
4 in.× 4 in.× 4 in.
4 inches times 4 inches times 4 inches
To find the dimensions of the cube box, we need to find the side length of the cube. Since the soap is spherical, the surface area of the soap is equal to the surface area of the cube it will be packaged in.
The formula for the surface area of a sphere is 4πr^2, where r is the radius.
Given that the surface area of the soap is 63.585 in^2, we can set up the equation:
4πr^2 = 63.585
Simplifying, we have:
r^2 = 63.585 / (4π)
r^2 ≈ 5.0625 / π
r^2 ≈ 1.6098
To find the radius, we take the square root of both sides:
r ≈ √1.6098
r ≈ 1.27
Now that we have the radius, we can find the side length of the cube box, which is equal to twice the radius:
side length ≈ 2 * 1.27
side length ≈ 2.54
Therefore, the dimensions of the cube box should be approximately 2.54 inches on each side.
None of the given responses match the correct dimensions of the cube box.