1. The problem statement, all variables and given/known data A right circular cone of base radius r and height h has a total surface area S and volume V . Show that 9V2=r2(S2-2pir2S) . (i can do this part) . Hence or otherwise , show that for a fixed surface area S , the maximum volume of the cone occurs when its semi-vertical angle , theta is given by tan theta=1/2(root 2) 3. The attempt at a solution From the proven equation , 9V2=r2(S2-2pir2S) Differentiate this wrt to r , dV/dr=(2S2r-8pi Sr3)/(18V) dV/dr=0 , S=4pi r2 , substitue S with the area of cone , then tan theta=r/h=1/(2 root 2) This is my question , how do i prove that its a maximum ?