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 21 inches 40.5 inches 40.5 inches 15 inches 15 inches 99 inches
The surface area of a cylinder can be calculated using the formula: SA = 2πr^2 + 2πrh, where r is the radius and h is the height.
Given that the diameter of each bucket is 12 inches, the radius (r) would be half of the diameter, so r = 6 inches.
Let's denote the height of the bucket as "h".
Since there are 5 buckets with the same dimensions, the total surface area can be calculated as: 5(2π(6)^2 + 2π(6)h) = 3,956.4
Solving for h:
5(2π(36) + 12πh) = 3,956.4
10π(36) + 60πh = 3,956.4
360π + 60πh = 3,956.4
420π = 3,956.4
60πh = 3,956.4 - 360π
60πh = 596.8
h = 596.8 / (60π)
h ≈ 100 / 3.14
h ≈ 31.847
Therefore, the height of one bucket is approximately 31.85 inches.
WRONG
I apologize for the mistake in my previous calculation. Let's correct that.
The surface area of a cylinder can be calculated using the formula: SA = 2πr^2 + 2πrh, where r is the radius and h is the height.
Given that the diameter of each bucket is 12 inches, the radius (r) would be half of the diameter, so r = 6 inches.
Let's denote the height of the bucket as "h".
Since there are 5 buckets with the same dimensions, the total surface area can be calculated as: 5(2π(6)^2 + 2π(6)h) = 3,956.4
Solving for h:
5(2π(36) + 12πh) = 3,956.4
10π(36) + 60πh = 3,956.4
360π + 60πh = 3,956.4
420π = 3,956.4
60πh = 3,956.4 - 360π
60πh = 616.4
h = 616.4 / (60π)
h ≈ 10.285
Therefore, the height of one bucket is approximately 10.29 inches.