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)

Question

(#1) 2.25 in. × 2.25 in. × 2.25 in .
(#2) 4.5 in. × 4.5 in. × 4.5 in .
(#3) 4 in. × 4 in. × 4 in
(#4) 1.2 in. × 1.2 in. × 1.2 in .

Answer 1

To find the dimensions of the cube box, we need to determine the volume of the spherical soap. The formula for the surface area of a sphere is 4πr^2, where r is the radius. Since the surface area of the soap is given as 63.585 in^2, we can set up the equation as follows:

4πr^2 = 63.585

Dividing both sides by 4π, we get:

r^2 = 63.585 / (4π)

Using 3.14 as the value of pi, we can simplify further:

r^2 ≈ 63.585 / (4*3.14)
r^2 ≈ 5.076

Taking the square root of both sides, we find:

r ≈ √5.076
r ≈ 2.25

So the radius of the soap is approximately 2.25 inches.

Now that we have the radius, we can find the diameter of the soap, which is twice the radius:

d ≈ 2 * 2.25
d ≈ 4.5

Finally, to find the dimensions of the cube box, we can use the diameter of the soap. The box should be slightly larger than the soap to allow for a snug fit. Therefore, the correct answer is (#2) 4.5 in. × 4.5 in. × 4.5 in.

Answer 2

Thanks

Answer 3

You're welcome! If you have any more questions, feel free to ask.