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Surface Area of Cylinders

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**Surface Area What does it mean to you?**

Does it have anything to do with what is in the inside of the prism? VOLUME (not surface area) is the amount a shape can hold inside. Surface area is found by finding the area of the circle and the area around the cylinder and adding it together.

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**Surface Area of Cylinders**

What is area? The amount of square units that will COVER a shape. How will the answer be labeled? Units2 because it is area!

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**SURFACE AREA of a CYLINDER.**

Imagine that you can open up a cylinder like so You can see that the surface is made up of two circles and a rectangle. The length of the rectangle is the same as the circumference of the circle!

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**EXAMPLE: Round to the nearest TENTH.**

Top or bottom circle A = πr² A = π(3.1)² A = π(9.61) A = 30.2 cm² Rectangle C = length The length is the same as the Circumference C = π d C = π(6.2) C = 19.5 cm Now the area A = lw A = 19.5(12) A = 234 cm² Now add: = SA = in²

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**2πr = πd SA = 2πr² + πd ·h This could be written a different way.**

A = πr² (one circle) This is the area of the top and the bottom circles. 2πr = πd So this formula could be written: SA = 2πr² + πd ·h

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**There is also a formula to find surface area of a cylinder. **

Some people find this way easier: SA = 2πrh + 2πr² SA = 2π(3.1)(12) + 2π(3.1)² SA = 2π (37.2) + 2π(9.61) SA = π(74.4) + π(19.2) SA = SA = in² The answers are REALLY close, but not exactly the same. That’s because we rounded in the problem.

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Now It’s YOUR Turn! I think I can!

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