Question

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Answer 1

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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Answer 2

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