I have a question about maths.
Calculate the radius of the cone, if Area = 9π and Volume = 2π.
I have tried turning around virtually everything, but cannot seem to succeed. Basically what I did was to try and equalize the area of the circle in the area formula with the area of the circle in the volume formula, I have also tried using the Pythagoras theorem to replace s with r and h, but I always end up with two variables in a single equation. The two equations that I kinda "derived" with the data are:
9 = r² + rs … from area
6 = r²h … from volume
Base formulas as a reminder:
A = πr² + πrs … where s is the length of the side and r is the radius
V = (πr² * h) / 3
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$\begingroup$From $$V=\frac{1}{3}\pi r^2h$$ we get $$h=\frac{3V}{\pi r^2}$$ and $$A=\pi r^2+\pi r\sqrt{r^2+h^2}$$and you have to solve$$A=\pi r^2+\pi r\sqrt{r^2+\frac{9V^2}{\pi^2 r^4}}$$squaring we get$$A^2-2A\pi r^2=\frac{9V^2\pi}{r^2}$$you can solve a quartic$$r=1/2\,{\frac {\sqrt {A\pi\, \left( {A}^{2}+\sqrt {-72\,A{\pi}^{2}{V}^{2 }+{A}^{4}} \right) }}{A\pi}} $$
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