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
To find the height of each bucket, we first need to calculate the surface area of one bucket.
The surface area of a cylinder is given by the formula:
A = 2πr(r + h) + πr^2, where r is the radius and h is the height.
Given that the diameter of the bucket is 12 inches, the radius, r, is half of the diameter, so r = 12/2 = 6 inches.
Substitute r = 6 inches into the formula:
A = 2*3.14*6(6 + h) + 3.14*6^2
A = 37.68(6 + h) + 113.04
A = 226.08 + 37.68h + 113.04
A = 339.12 + 37.68h
Now, we know that the total surface area of all 5 buckets is 3,956.4 square inches, so:
5(339.12 + 37.68h) = 3,956.4
1,695.6 + 188.4h = 3,956.4
188.4h = 2,260.8
h = 12 inches
Therefore, the height of each bucket is 12 inches.