SOLUTION: Given the formula A=2*pi*r(r+h), solve for h.

Algebra ->  College  -> Linear Algebra -> SOLUTION: Given the formula A=2*pi*r(r+h), solve for h.      Log On


   



Question 1079891: Given the formula A=2*pi*r(r+h), solve for h.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

A%22%22=%22%222pi%2Ar%28r%2Bh%29

Distribute 2pr into the parentheses (r+h)
to remove the parentheses:

A%22%22=%22%222pi%2Ar%5E2%2B2pi%2Arh

Get the term that does not contain h off the right side, by
subtracting 2pr2 from both sides:


A-2pi%2Ar%5E2%22%22=%22%222pi%2Arh

Divide both sides by what is multiplied by h on the right side,
which is 2pr

%28A-2pi%2Ar%5E2%29%2F%282pi%2Ar%29%22%22=%22%22%282pi%2Arh%29%2F%282pi%2Ar%29

We have to be careful here.  Although it is perfectly correct
to cancel 2pr on the right side, since EVERYTHING IS MULTIPLIED.
However, we MUST NOT CANCEL anything on the left side because 
the numerator is a SUBTRACTION, not a MULTIPLICATION.  So 
cancel on the right, but leave the left side as it is.

%28A-2pi%2Ar%5E2%29%2F%282pi%2Ar%29%22%22=%22%22%28cross%282pi%2Ar%29h%29%2F%28cross%282pi%2Ar%29%29

%28A-2pi%2Ar%5E2%29%2F%282pi%2Ar%29%22%22=%22%22h

Edwin