Question

How do you solve for l in `S= (pi r^2 )+ (pi r l)`?

Answer 1

See the entire solution process below:

Explanation:

First, factor out a `pir` from each term in the right side of the equation:

`S = pir(r + l)`

Next, divide each side of the equation by `color(red)(pir)` to eliminate the coefficient while keeping the equation balanced:

`S/color(red)(pir) = (pir(r + l))/color(red)(pir)`

`S/(pir) = (color(red)(cancel(color(black)(pir)))(r + l))/cancel(color(red)(pir))`

`S/(pir) = r + l`

Now, subtract `color(red)(r)` from each side of the equation to solve for `l`:

`-color(red)(r) + S/(pir) = -color(red)(r) + r + l`

`-r + S/(pir) = 0 + l`

`-r + S/(pir) = l`

`l = -r + S/(pir)`

If you want the right side of the equation to be over a common denominator you can multiply `-r` by `(pir)/(pir)` giving:

`l = ((pir)/(pir) xx -r) + S/(pir)`

`l = (-pir^2)/(pir) + S/(pir)`

`l = (-pir^2 + S)/(pir)`

`l = (S - pir^2)/(pir)`

The solution is: `l = -r + S/(pir)` or `l = (S - pir^2)/(pir)`