# Surface Area of Cylinders.

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Surface Area of Cylinders

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.

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!

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!

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

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

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.

Now It’s YOUR Turn! I think I can!

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