SOLUTION: What's the Surface Area of a right cylinder with a radius of 7 and the height 15

Question 622132: What's the Surface Area of a right cylinder with a radius of 7 and the height 15
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there--
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We want to know the surface area of a right cylinder with a radius of 7 units and a height of 15 units.
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A right cylinder is a 3-D geometric solid rough the shape of a soup can. The surface area is the sum of the circular top and bottom (like the lids on a soup can) and the rectangular side of the cylinder (where the label goes on a soup can.)
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So, we need the area of two circles with radius 7. The formula for the area of a circle is

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Substitute 7 for r and we get

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Now we need the area of the side of the cylinder. The formula for the area of a rectangle is

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In this case the width W is the height of the cylinder, 15. The length W is the distance around the circular top. THis is also called the circumference of the circle. The formulae for the circumference is

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Substitute 7 for r and we have

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Now we have the width and length for the rectangular side of the cylinder, so

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Substitute the known values and find the area.

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So the surface area is

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Simplify.

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This is the exact answer for the surface area. Depending on the instructions you were given, you might also want an approximation. Pi is roughly 3.14. We'll substitute 3.14 for pi.
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The surface area of the cylinder is about 967.12 square units.

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