Geometry

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# Surface Area of a Cylinder

## Cylinder Surface Area Formula

The formula for surface area of a cylinder is given as:**SA = 2πrh + 2πr ^{2}**

Where

*SA*is the surface area,

*r*is the radius of the base circle, and

*h*is the height of the cylinder.

### Example Problems

**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 + 2πr^{2}

SA = 2π(10)(20) + 2π(10^{2}) = 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 = h^{2}

r^{2} = h^{2}

2.) Now let’s plug what we know into the surface area formula and solve for h.

SA = 2πrh + 2πr^{2}

24 = 2πh^{2} + 2πh^{2}

24 = 4πh^{2}

1.910 = h^{2}

h = 1.382

3.) **The height of the cylinder is 1.382 meters.**