Question

Arya has 5 separate buckets with lids, each the same size and in the shape of a cylinder. If the total surface area of all 5 buckets is 3,956.4 square inches and the diameter of each bucket is 12 inches, what is the height of 1 bucket? Use 3.14 for π .(1 point) Responses 21 inches 99 inches 15 inches 40.5 inches

Answer 1

To find the height of one bucket, we first need to calculate the surface area of one bucket.

The surface area of a cylinder is calculated as:
2πr^2 + 2πrh, where r is the radius and h is the height.

Given the diameter of each bucket is 12 inches, the radius (r) is half of the diameter, so r = 6 inches.

Plugging in the values:
Total surface area = 5 * (2π(6)^2 + 2π(6)h)
3,956.4 = 5 * (2π(36) + 12πh)
3,956.4 = 5 * (72π + 12πh)
791.28 = 360π + 60πh
791.28 = 420π + 60πh
371.28 = 60πh
h = 371.28 / (60π)
h ≈ 7.77 inches

Therefore, the height of one bucket is approximately 7.77 inches.

Answer 2

THIS IS NOT ONE OF THE RESPONSES

Answer 3

I apologize for the error in my calculation. Let's correct it.

Given:
- Total surface area of all 5 buckets = 3,956.4 square inches
- Diameter of each bucket = 12 inches

First, let's find the radius (r) of each bucket:
Radius (r) = Diameter / 2 = 12 / 2 = 6 inches

Now, we can calculate the lateral surface area of one bucket:
Lateral Surface Area of a Cylinder = 2πrh

Given the total surface area of all 5 buckets:
Total Lateral Surface Area of 5 Buckets = 5 * 2πrh = 10πrh

10πrh = 3,956.4
60πh = 3,956.4
h = 3,956.4 / (60π)
h ≈ 10 inches

Therefore, the height of one bucket is approximately 10 inches. None of the options provided match the correct answer, but the correct height is approximately 10 inches.