ShmoopTube

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Surface Area of Cylinders, a la Shmoop.

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You've adopted an elephant in Africa.

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…but the holidays are coming up and you want to do something special... so you knit him a [Woman in a rocking chair]

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trunk warmer.

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You don't want it to get damaged by the UPPS... the United Pachyderm Parcel Service... so you need

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to ship it in a sturdy tube. [Woman holding her trunk warmer]

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

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You think you have enough cardboard to make the tube yourself, but you're not totally sure... [The tube design drawn]

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How much cardboard do you need?

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Here are your potential answers: A cardboard shipping tube is the shape of a cylinder.

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

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Well fortunately, there's a formula for finding the surface area of a cylinder. [The formula is written out]

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But first, let's break down what the cylinder looks like when it's flattened... [Elephant sitting on the cylinder]

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First, we'll need to find the area of each of those circles. [The circles are highlighted with arrows]

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

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Well our radius we know already is 3, so our formula will be pi times three squared. [The formula with the values inserted]

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Three squared is nine.

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Pi is approximately three-point-one-four,

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so three-point-one-four times nine is twenty-eight-point-two-six. [The working is shown]

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We have two circles, so we'll then need to double that number.

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

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So far this is easier than knitting that trunk warmer... [Old woman knitting in her rocking chair]

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But we still have to find the area of the middle part of the cylinder...

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… which is a rectangle when rolled flat. [The elephant sits on the cyclinder again]

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To find this area, we'll need to multiply the height, which we know is five, by the

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circumference of the circle. [The circumference of the circle is shown with an arrow]

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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 in this case, is eighteen-point-eight-four. [The working is shown]

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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.

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To get the total surface area, we just add 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. [The total surface area formula is used]

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So the answer is C.

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Sounds like a lot of cardboard.

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Good thing you've bought quite a few nasal hair trimmers over the years. [Pile of nasal hair trimmer boxes]

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