How do you find surface area of a cylinder if you are only given the volume?

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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If you are given the volume of a cylinder that means that you have information that you can use for the surface area. 

The formula for volume of a cylinder is `(pir^2 times h)`

Note how the volume formula is similar to the area formula for a circle `(pir^2)` times the height. As we have 2 circles, our surface area will be `2pi r^2`

To find the surface area you need the area of each surface which is 2 circles (top and bottom) and the depth of the cylinder which is the circumference `(2 pi r)` times the height: `(2pi r times h)`

Therefore you can work backwards from volume because you need a lot of the same information.

`therefore S.A.= 2 pi rh +2 pi r^2`  

However, we still have 2 unknowns so a question would usually include another piece of information; for example, that radius is twice height or something to link radius to height. 

Ans: Use formula `S.A.= 2 pirh + 2pir^2`  and express height in terms of radius or radius in terms of height depending on the question.