A cylindrical can, open at the top, is to hold 400cm^3 of liquid. Find the height, h, and the radius, r, that minimizes the amount of material needed to manufacture the can.

Question

A cylindrical can, open at the top, is to hold 400cm^3 of liquid. Find the height, h, and the radius, r, that minimizes the amount of material needed to manufacture the can.

Answer 1

400= hpir^2

h=400/pir^2

an open top cylindrical can

area = bottom + side

area = pir^2 +2pirh

= pir^2 +800/r

area' = 2pir -800/r^2= 0

pir^3 =400

r^3= 400/pi

r = (400/pi)^(1/3)=5.03 cm. = material minimizing radius

h=400/pir^2=400/pi(5.03)^2

h= 5.03.cm.= material minimizing height