Problem 1:
What is the surface area of a cylinder with a diameter of 20 and a height of 20?

Solution:
1.) Let’s convert diameter to radius. D = 2r, 20 = 2r, so r = 10.
2.) Now let’s plug the radius and height into the surface area formula.
SA = 2πrh + 2πr²
SA = 2π(10)(20) + 2π(10²) = 2π(200) + 2π(100)
SA = 1,884.956
4.) The surface area is 1,884.956.

Problem 2:
A cylinder is measured to have a surface area of 24 square meters. It’s height and radius are equal. What is the height of the cylinder?

Solution:
1.) Let’s set up relations between height and radius that we can substitute into the formula.
h = r
rh = h²
r² = h²
2.) Now let’s plug what we know into the surface area formula and solve for h.
SA = 2πrh + 2πr²
24 = 2πh² + 2πh²
24 = 4πh²
1.910 = h²
h = 1.382
3.) The height of the cylinder is 1.382 meters.