If the sum of slant height, height and radius is (9+3\sqrt{3}) cm, then what is the volume of the cone?

Explanation

Given \frac{r}{l} = \frac{\sqrt{3}}{2} and \frac{h}{l} = \frac{1}{2}, substituting into l+h+r = 9+3\sqrt{3} gives l(1.5 + 0.5\sqrt{3}) = 3(3+\sqrt{3}), yielding l=6. Then r=3\sqrt{3} and h=3. Volume = \frac{1}{3}\pi r^2 h = 27\pi cm^3. Option A is missing \pi due to a typo in the paper, but corresponds to the correct numerical coefficient.

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