SOLUTION: Let L = lateral area. Given L = pi•r•sqrt{r^2 + h^2}, solve for h.

Algebra ->  Surface-area -> SOLUTION: Let L = lateral area. Given L = pi•r•sqrt{r^2 + h^2}, solve for h.       Log On


   

Question 1208903: Let L = lateral area.

Given L = pi•r•sqrt{r^2 + h^2}, solve for h.
Answer by ikleyn(52852) About Me  (Show Source):
You can put this solution on YOUR website!
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Let L = lateral area  of  a  cone.

Given   L = pi•r•sqrt{r^2 + h^2},  solve for  h.
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Your starting formula is 

    L = pi%2Ar%2Asqrt%28r%5E2+%2B+h%5E2%29.


Divide both sides by pi%2Ar

    L%2F%28pi%2Ar%29 = sqrt%28r%5E2%2Bh%5E2%29.


Square both sides

    %28L%2F%28pi%2Ar%29%29%5E2 = r%5E2+%2B+h%5E2.


Express  h%5E2

    h%5E2 = %28L%2F%28pi%2Ar%29%29%5E2 - r%5E2


Take the square root of both sides and use its positive value

    h = sqrt%28%28L%2F%28pi%2Ar%29%29%5E2-r%5E2%29.


It is the desired expression for h.    ANSWER

Solved.