Solve for #h^2#: #r = pi sqrt (r^2 + h^2)# ? assume all variables represent positive real numbers.

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Answer 1 · 2017-04-12T18:59:25

#r^2/pi^2 - r^2 = h^2#

Square both sides:

#r^2= pi^2(r^2 + h^2)#

#r^2/pi^2 = r^2 + h^2#

#r^2/pi^2 - r^2 = h^2#

Hopefully his helps!

Answer 2 · 2017-04-12T19:01:02

Please see the explanation.

Given: #r = pi sqrt (r^2 + h^2)#

Square both sides:

#r^2= pi^2(r^2 + h^2)#

#r^2/pi^2 = r^2 + h^2#

#h^2 = (1/pi^2-1)r^2#

#h^2 ~~ -0.899r^2#

Oh! NO! #h^2# must be negative and, therefore, h must be imaginary.