What is the optimal ratio of height to radius for a cone with minimum cost?

[BayernBlues]

Homework Statement

http://img128.imageshack.us/img128/3923/12mx7.png

Homework Equations

The Attempt at a Solution

c=0.06(pie)r^2+0.06(pie)r(k/pie(r^2))

c'=0.06(pie)r - 0.06kr^-2
r^3=k^1/3 / (pie^1/3)

h/r= 1/1

I'm not sure if what I did here is right. I didn't put all the steps up there.

 

[amanmahadeshwar]

ANSWER DIRECT FROM INDIA

yup you have the right answer r/h does = 1

if you briefly want the steps just to check

COST = 0.12*(pie)*r*h + 0.06*(pie)*r^2

find derivative U get

-(K * 0.12)/(r^2) + 0.12*(pie)*r

equate this derivative to zero

thus -K + (pie)*(r^3) = 0

THUS (pie)*(r^3) = K


but K = (p)*(r^2)*h

thus r = h