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 .

Answer 1

The formula for the surface area of a cylinder is:

Surface Area = 2πr^2 + 2πrh

Since all 5 buckets are the same size, we can just focus on finding the surface area of 1 bucket. We know that the diameter is 12 inches, so the radius (r) is half of that: 12/2 = 6 inches.

We are given that the total surface area of all 5 buckets is 3,956.4 square inches, so the surface area of 1 bucket would be:

3956.4 / 5 = 791.28 square inches

Now we can plug in the values we know into the surface area formula and solve for the height (h):

791.28 = 2 * 3.14 * 6^2 + 2 * 3.14 * 6h
791.28 = 226.08 + 37.68h
565.2 = 37.68h
h = 565.2 / 37.68
h = 15 inches

So, the height of 1 bucket is 15 inches.