Question

Marcus is making spherical soaps to sell in his online store. The surface area of a soap is 63.585 in². 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? a. 2.25 in. ×2.25 in. ×2.25 in b. 1.2 in. ×1.2 in. ×1.2 in c. 4 in. ×4 in. ×4 in. d. 4.5 in. ×4.5 in. ×4.5 in.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the dimensions of the cube box, we first need to find the volume of the spherical soap. The formula for the surface area of a sphere is 4πr², so we have:

4πr² = 63.585
r² = 63.585 / 4π
r² = 5.08
r = √5.08
r ≈ 2.25 inches

Now that we have the radius of the sphere, we can calculate the volume of the sphere:

V = (4/3)πr³
V = (4/3)π(2.25)³
V ≈ 38.25 in³

Since the cube box will fit snugly around the spherical soap, the volume of the box should be equal to the volume of the soap. Therefore, the dimensions of the cube box should have a volume of 38.25 in³.

The only option that has a volume close to 38.25 in³ is option a. 2.25 in. ×2.25 in. ×2.25 in.

Therefore, the correct answer is a. 2.25 in. ×2.25 in. ×2.25 in.