Find the dimensions of the right circular cylinder with top

Solution

V0 = pi r^2h h = V0/pi r^2 S = 2pi rh + pi r^2 S = 2pi r/(V0/pi r^2) + pi r^2 S = 2(pi)^2r^3/V0 + pi r^2 dS/dr = 6(pi)^2r^2/V0 + 2pi r = 0 2pi r[3pir/V0 + 1] = 0 3pir/V0 + 1 = 0 3pir = -V0 r = -V0/3pi since it cannot be negative r = V0/3pi.......(1) h = V0/pir^2 h = Vo/pi(Vo/3pi)^2 h = 9pi/Vo