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)

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.

Thanks

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

To find the dimensions of the cube box, we first need to determine the radius of the soap. We know that the surface area of the soap is given by the formula:

Surface area = 4πr²

Here, the surface area is given as 63.585 in², so we can rearrange the formula to solve for the radius:

63.585 in² = 4πr²

Dividing both sides by 4π:

r² = 63.585 in² / (4π)

Using the value of pi (π = 3.14):

r² = 5.0837 in²

Taking the square root of both sides:

r ≈ √(5.0837 in²) ≈ 2.257 in

Now that we have the radius, we know that the diameter of the soap is 2r = 2 × 2.257 in ≈ 4.514 in. Since the cube box needs to fit snugly around the soap, the dimensions of the cube should be equal to or slightly larger than the diameter of the soap.

Looking at the given options:
1) 2.25 in. × 2.25 in. × 2.25 in. - This is slightly smaller than the diameter of the soap, so it will not fit snugly.
2) 4.5 in. × 4.5 in. × 4.5 in. - This is equal to the diameter of the soap, so it will fit snugly.
3) 4 in. × 4 in. × 4 in. - This is slightly smaller than the diameter of the soap, so it will not fit snugly.
4) 1.2 in. × 1.2 in. × 1.2 in. - This is significantly smaller than the diameter of the soap, so it will not fit snugly.

Therefore, the correct answer is option (#2) 4.5 in. × 4.5 in. × 4.5 in.