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.
First, we need to find the surface area of 1 bucket.
The formula for the surface area of a cylinder is:
SA = 2πr(r + h)
Given that the diameter of each bucket is 12 inches, the radius (r) is half of that, so r = 6 inches.
Let's plug in the values:
SA = 2 * 3.14 * 6(6 + h)
SA = 37.68 + 37.68h
Since we have 5 buckets, the total surface area of all 5 buckets is:
5 * (37.68 + 37.68h) = 3,956.4
188.4 + 188.4h = 3,956.4
188.4h = 3,768
Now, we can solve for h:
h = 3,768 / 188.4
h = 20
Therefore, the height of 1 bucket is 20 inches.