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 in.× 4 in.× 4 in. 4 inches times 4 inches times 4 inches 2.25 in. × 2.25 in. × 2.25 in. 2.25 inches times 2.25 inches times 2.25 inches 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.
To find the dimensions of the cube box that will fit the spherical soap snugly, we need to find the diameter of the soap first.
The surface area of a sphere is given by the formula SA = 4πr², where SA is the surface area and r is the radius of the sphere.
Given that the surface area of the soap is 63.585 in², we can rearrange the formula to solve for the radius:
63.585 = 4 × 3.14 × r²
Divide both sides by (4 × 3.14):
r² = 63.585 / (4 × 3.14)
r² = 5.09
Take the square root of both sides:
r ≈ √5.09
r ≈ 2.259
Since the cube box needs to snugly fit the soap, the side length of the cube needs to be equal to twice the radius of the soap.
Side length of the cube = 2 × r
Side length of the cube ≈ 2 × 2.259
Side length of the cube ≈ 4.518
Therefore, the dimensions of the cube box should be approximately 4.518 inches × 4.518 inches × 4.518 inches, which can be rounded to 4.5 inches × 4.5 inches × 4.5 inches.