Posted by MM on Thursday, December 6, 2012 at 8:28pm.
with radius r and height h,
pi r^2 h + 2/3 pi r^3 = v
so,
h = 3(v - pi r^2)/(2pi r^3)
a = pi r^2 + 2pi r h + 2pi r^2
= 3pi r^2 + 2pi r h
= 3pi r^2 + 3(v - pi r^2)/r^2
= 3pi r^2 - 3pi + 3v/r^2
da/dr = 6pi r - 6v/r^3
dv/dr = 0 when r^4 = v/pi
a(∜(v/pi)) = 3pi√(v/pi) - 3pi + 3√(pi*v)
= 3√pi (2√v - 1)
as usual, double-check the arithmetic and the algebra. I'm pretty sure about the calculus.
thanks a ton.
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