Surface Area of a Cylinder

Cylinder Surface Area Formula

The formula for surface area of a cylinder is given as:
SA = 2πrh + 2πr2
Where SA is the surface area, r is the radius of the base circle, and h is the height of the cylinder.

surface area of a cylinder

Example Problems

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

Result :

Worksheet 1


Cheat sheet


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