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

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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.

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial