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
Answers
GPT 3.5
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.
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.
THIS IS NOT ONE OF THE RESPONSES
GPT 3.5
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.
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.
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