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)

Answer 1

First, we need to calculate the total surface area of one bucket.

The total surface area of a cylinder can be calculated using the formula:

SA = 2πr^2 + 2πrh

Where:
SA = Surface Area
r = radius of the base of the cylinder
h = height of the cylinder

Given that the diameter of each bucket is 12 inches, the radius (r) of each bucket is half of the diameter, so r = 6 inches.

We also know that the total surface area of all 5 buckets is 3,956.4 square inches.

Therefore, the surface area of 1 bucket can be calculated as:

SA = 2(3.14)(6^2) + 2(3.14)(6)h
SA = 2(3.14)(36) + 2(3.14)(6)h
SA = 226.08 + 37.68h

Now we know that the total surface area of all 5 buckets is 3,956.4 square inches. So:

5(226.08 + 37.68h) = 3,956.4
1,130.4 + 188.4h = 3,956.4
188.4h = 2,826
h = 15

Therefore, the height of one bucket is 15 inches.