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

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Answer 1 · 2017-02-26T18:34:17

See the entire solution process below:

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

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