# Surface Area of Cylinders

Haven't you always wondered how much cardboard it takes to encase a trunk warmer for your pet elephant?

Geometry | Area and Volume |

Language | English Language |

Math | Geometry |

Pre-Algebra | Basic Geometry |

### Transcript

United Pachyderm Parcel Service... you need to ship it in a sturdy tube.

The trunk warmer will fit perfectly in a tube with radius three and height five.

You think you have enough cardboard to make the tube yourself. How much cardboard do you

need?

Here are your options: A cardboard shipping tube is a cylinder.

So to figure this problem out, we'll need to find the Surface Area of a Cylinder.

The finished product will look like this, but how do we find the area of it?

Just like you have a formula for knitting an elephant trunk warmer...

You can find anything on Pinterest...

There's a formula for finding the surface area of a cylinder.

But first, let's break down what the cylinder looks like when it's flattened...

Like it will be after your elephant sits on it.

First, we'll need to find the area of each of those circles.

The formula for finding the area of a circle is pi times the radius squared.

Our radius is three, so our formula will be pi times three squared.

Three squared is three times three, or nine.

Pi is approximately three-point-one-four, so three-point-one-four times nine is twenty-eight-point-two-six.

We have two circles, so we'll then need to double that number. Twenty-eight-point-two-six

times two is fifty-six-point-five-two.

This is easier than knitting that trunk warmer... it took forever to figure out what "purling"

means. But we still have to find the area of the

middle part of the cylindrical part of the cylinder...

... which is a rectangle when squashed flat. To find this area, we'll need to multiply

the height, which we know is five, by the circumference of the circle.

This makes up the top and bottom edge of the rectangle.

We can find out what this is by using the simple formula two pi "r."

Two times pi is approximately six-point-two-eight.

Six-point-two-eight times "r," which is three, is eighteen-point-eight-four.

Now we just multiply that by the height, five, to get the surface area of the middle part

of the cylinder, which is ninety-four-point-two. To get the total surface area, we just add

our two numbers together.

Fifty-six-point-five-two plus ninety-four-point-two equals one-hundred-fifty-point-seven-two.

So the answer is C.

Sounds like a lot of cardboard. Good thing you've bought quite a few nasal hair trimmers

over the years. The trunk warmer is knitted, the tube is made,

and off it goes.

We hope your elephant appreciates all the hard work you did.