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thereddevils
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Homework Statement
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)
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 ?