Question

A theme park has a ride that is located in a cylinder with a height of 12 yards. The ride goes around the outside of the​ cylinder, which has a circumference of 514.35 yards. What is the surface area of the​ cylinder? Estimate to the nearest​ hundredth, using 3.14 for pi. Apply the formula for surface area of a cylinder.

Answer 1

The formula for the surface area of a cylinder is:

S = 2πrh + 2πr²

where S is the surface area, r is the radius, and h is the height.

We are given that the height of the cylinder is 12 yards and the circumference is 514.35 yards.

The circumference of a cylinder is given by the formula:

C = 2πr

where C is the circumference and r is the radius.

Substituting the given value of the circumference, we get:

514.35 = 2πr

r = 514.35 / (2π)

r ≈ 81.97

Now we can use the formula for surface area:

S = 2πrh + 2πr²

Substituting the given values, we get:

S = 2(3.14)(81.97)(12) + 2(3.14)(81.97)²

S ≈ 50,684.97

Therefore, the surface area of the cylinder is approximately 50,684.97 square yards.