ShmoopTube

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

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

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educated...

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

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

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

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

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

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need?

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

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

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

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

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You can find anything on Pinterest...

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

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

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Like it will be after your elephant sits on it.

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

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

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

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Three squared is three times three, or nine.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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our two numbers together.

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

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So the answer is C.

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

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

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and off it goes.

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

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