Calculus
posted by MM on .
A solid is formed by adjoining one hemisphere to the top of a cylinder. The total volume of the solid is V (treat as a constant) cubic centimeters. Find the minimum surface area of the solid in terms of V.

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, doublecheck the arithmetic and the algebra. I'm pretty sure about the calculus. 
thanks a ton.