• # question_answer A conical tent is to accommodate 10 persons. Each person must have $6\text{ }{{m}^{2}}$ space to sit and $30\,\,{{m}^{3}}$ of air to breath. What will be the height of the cone? A)  37.5 m                        B)  150 m        C)  75 m               D)  None of these

Solution :

(d): Area of base $=6\times 10=60\,\,{{m}^{2}}$ Volume of tent $=30\times 10=300\,\,{{m}^{3}}$ Let the radius be = r, height = h, slant height = l $\therefore$ $\pi {{r}^{2}}=60\Rightarrow r=\sqrt{\frac{60}{\pi }}$ Also, $300=\frac{\pi {{r}^{2}}h}{3}$ $\Rightarrow$ $900=\pi .\frac{60}{\pi }.h$ $\Rightarrow$$h=15\,\,m$

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