square both sides
A^2=(PI*r)^2 (h^2-r^2)
divide both sides by PI^2
(A/PI)^2 -r^2h^2 +r^4=0 define a new variable, u=r^2
u^2-uh^2+(A/PI)^2=0 now use the quadratic formula
u=(h^2+-sqrt(h^4-4A^2/PI^2)/2
but u=r^2, so for r, take the square root of u above.
Note there are two solutions, life is not so simple in these equations.
A=πr√(h^2-r^2)
make "r" the subject of the formula
show workings
#thanks
6 answers
Very interesting
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thug CNN
Make r the subject of the formula in A=pie r square root of h rest to the power 2-r rest to the power 2
6c(3e+2d)