an open topped cylingrical pot is to have a volume of 125 cm^3. determine the minimal possible amount of material used in making this pot.( neglect the thickness of the material as well as possible waste)
a = pi r^2 + 2pi r h
v = pi r^2 h = 125
so,
h = 125/(pi r^2)
a = pi r^2 + 2pi r (125/(pi r^2))
a = pi r^2 + 250/r
da/dr = 2pi r - 250/r^2
da/dr = 0 when
2pi r - 250/r^2 = 0
2pi r^3 = 250
r = 5/cbrt(pi) = 3.414 cm
a = 109.8 cm^2