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
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
2.25 in. × 2.25 in. × 2.25 in.
To find the dimensions of the cube box, we need to calculate the side length (s) of the cube.
Given that the surface area of the soap is 63.585 in², the formula for the surface area of a sphere is 4πr², where r is the radius of the sphere.
Since a soap is spherical, the surface area is 4πr², which in this case is 63.585 in².
By rearranging the formula and substituting π with 3.14, we can find the radius (r):
4πr² = 63.585
r² = 63.585 / (4 * 3.14)
r² = 5.075
r ≈ √5.075
r ≈ 2.25
The diameter of the sphere (which is twice the radius) is 2 * 2.25 = 4.5 inches.
Since a cube has all equal sides, the dimensions of the cube box should be 4.5 in. × 4.5 in. × 4.5 in.