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 buckets is 3,956.4 square inches and the diameter of each buckets is 12 inches, what is the height of 1 bucket
First, let's find the surface area of 1 bucket.
The surface area of a cylinder is given by the formula:
SA = 2πr^2 + 2πrh
Where r is the radius of the cylinder and h is the height of the cylinder.
Given that the diameter of each bucket is 12 inches, the radius (r) 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 is 3,956.4 / 5 = 791.28 square inches.
Now, we can plug in the values we know into the formula:
791.28 = 2π(6)^2 + 2π(6)h
791.28 = 72π + 12πh
791.28 = 84π + 12πh
791.28 - 84π = 12πh
791.28 - 84π ≈ 504.16
504.16 ≈ 12πh
42.01 ≈ πh
h ≈ 13.38
Therefore, the height of 1 bucket is approximately 13.38 inches.