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 pi
First, let's calculate the total surface area of one bucket.
The formula for the surface area of a cylinder is given by:
Surface Area = 2πr( r + h)
Given that the diameter of each bucket is 12 inches, the radius (r) would be half of that, so r= 6 inches.
Now, we are given 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, plug in the values for r and the surface area into the formula and solve for h:
791.28 = 2 * 3.14 * 6 * (6 + h)
791.28 = 37.68 + 37.68h
753.60 = 37.68h
h = 753.60 / 37.68
h ≈ 20
Therefore, the height of one bucket is approximately 20 inches.