Prove that the volume
![V](/media/m/5/d/1/5d1544cc9c474ed7006c60d2c6dfebf6.png)
and the lateral area
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
of a right circular cone satisfy the inequality
![\left( \frac{6V}{\pi}\right)^2 \leq \left( \frac{2S}{\pi \sqrt 3}\right)^3](/media/m/6/2/8/6282ce6233d6953d25ebfd52740b8267.png)
When does equality occur?
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Prove that the volume $V$ and the lateral area $S$ of a right circular cone satisfy the inequality
$$\left( \frac{6V}{\pi}\right)^2 \leq \left( \frac{2S}{\pi \sqrt 3}\right)^3$$
When does equality occur?