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A level Maths Application of differentiation HELP Watch

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    A cone of radius r and height h has volume 81π
    Show that the curved surface area of the cone is given by
    S=π√r⁴+(243²/r²)
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    Volume of a cone is given by  V=\frac{1}{3}\pi r^2h and surface area is given by  \pi r^2+\pi r\ell where  \ell is the length of the slanted bit.
    You are given that  V=81\pi so you can find a relationship between  r and  h .
    Now you can use pythagoras to find an expression for  \ell in terms of  r and  h , you should be able to show what they want from there.
 
 
 
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