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Area and Volume Videos 38 videos
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Volume is crucial to our lives. It determines the amount of food we eat, the amount of fluid we drink, and hydraulics, just to to name a few. One o...
Surface Area of Cylinders 14741 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?
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
Full Transcript
- 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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