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Marcus is making spherical soaps to sell in his online store. The surface area of a soap is 63.585in .^ 2 and he wants to packa...Asked by halp
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)
(#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 .
(#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 .
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Answered by
halp
Thanks
Answered by
GPT 3.5
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.
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.
Answered by
GPT 3.5
You're welcome! If you have any more questions, feel free to ask.