Solve for h. `A=pirsqrt(h^2+r^2)` Please explain how you arrive at the answer.Thanks

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lemjay | High School Teacher | (Level 3) Senior Educator

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`A=pirsqrt(h^2+r^2)`

First, isolate `sqrt(h^2+r^2)` . To do so, divide both sides by `pi r` .

`A/(pir)=(pirsqrt(h^2+r^2))/(pir)`

`A/(pir)=sqrt(h^2+r^2)`

Then, eliminate the radical. So, square both sides of the equation.

`(A/(pir))^2=(sqrt(h^2+r^2))^2`

`(A/(pir))^2=h^2+r^2`

To have h^2 only at the right side, subtract both sides by r^2.

`(A/(pir))^2-r^2=h^2+r^2-r^2`

`(A/(pir))^2-r^2=h^2`

And, to have h only, take the square root of both sides of equation.

`sqrt((A/(pir))^2-r^2)=sqrt(h^2)`

`sqrt((A/(pir))^2-r^2)=h`

Then, simplify left side.

`sqrt(A^2/(pi^2r^2)-r^2)=h`

`sqrt(A^2/(pi^2r^2)-(pi^2r^4)/(pi^2r^2))=h`

`sqrt((A^2-pi^2r^4)/(pi^2r^2))=h`

`(sqrt(A^2-pi^2r^4))/(pir)=h`

 

Hence, `h=(sqrt(A^2-pi^2r^4))/(pir)` .

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