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 40.5 inches 40.5 inches 99 inches 99 inches 15 inches 15 inches 21 inches
To find the height of one bucket, we first need to find the surface area of one bucket.
Given that the diameter of each bucket is 12 inches, the radius (r) of each bucket is half of the diameter, which is 6 inches.
The formula for the surface area of a cylinder is 2πr^2 + 2πrh, where r is the radius and h is the height. Since the surface area of one bucket is given, we can set up the following equation:
2π(6)^2 + 2π(6)h = 3,956.4
72π + 12πh = 3,956.4
84πh = 3,956.4
h = 3,956.4 / (84π)
h ≈ 14.93
So, the height of one bucket is approximately 14.93 inches.