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 99 inches 99 inches 15 inches 15 inches 40.5 inches 40.5 inches 21 inches
To find the total surface area of one bucket, we first calculate the surface area of the sides and the surface area of the top and bottom.
The formula for the lateral surface area of a cylinder is:
L = 2πrh
The formula for the top and bottom surface area of a cylinder is:
B = 2πr^2
Given that the diameter is 12 inches, the radius (r) is half the diameter, so r = 6 inches.
Substituting r = 6 and using π = 3.14, we have
L = 2 * 3.14 * 6 * h = 37.68h
B = 2 * 3.14 * 6^2 = 226.08
The total surface area of one bucket is:
Total surface area = L + 2B = 37.68h + 2(226.08) = 37.68h + 452.16
Given the total surface area for 5 buckets is 3,956.4 square inches:
5(37.68h + 452.16) = 3,956.4
188.4h + 2,260.8 = 3,956.4
188.4h = 1,695.6
h = 1695.6 / 188.4
h ≈ 9
Therefore, the height of one bucket is about 9 inches.