How to design the bottom radius and height of a cylindrical oil drum with a volume of V in order to save the available materials to the greatest extent? Solve the problem of high numbers.

Assume that the bottom radius of the oil drum is r and the height is h.

rule

V=PI*r squared h

Find the square of h = v/pi * r.

Oil drum surface area S= bottom surface+side surface =π* r square +2PI*r*h

S=PI*r square +2PI*r*V/PI*r square.

The question now becomes r=? S gets the minimum value.

DS/dr= self-help =0

r=?

H= V/PI*r squared =?

end