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