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Surface Area of Cylinders 14740 Views


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Description:

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

Language:
English Language

Transcript

00:05

Surface Area of Cylinders, a la Shmoop. You've adopted an elephant in Africa.

00:14

Normally you send a small amount of money every month to keep him fed, clothed, and

00:18

educated...

00:19

...but the holidays are coming up and you want to do something special... knit him a

00:25

trunk warmer. So it doesn't get damaged by the UPPS... the

00:29

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

00:34

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

00:39

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

00:44

need?

00:45

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

00:52

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

00:57

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

01:01

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

01:04

You can find anything on Pinterest...

01:07

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

01:10

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

01:14

Like it will be after your elephant sits on it.

01:16

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

01:20

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

01:25

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

01:30

Three squared is three times three, or nine.

01:34

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

01:42

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

01:50

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

01:56

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

02:00

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

02:03

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

02:06

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

02:11

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

02:16

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

02:19

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

02:24

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

02:29

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

02:35

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

02:40

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

02:46

our two numbers together.

02:48

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

02:55

So the answer is C.

02:57

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

03:01

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

03:07

and off it goes.

03:08

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

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