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A conical tent is to accommodate $10$ persons. Each person must have $6$ $m$$^{2}$ space to sit and $30\;m^{3}$ of air to breath. What will be height of cone ?

1. $37.5$ $m$
2. $150$ $m$
3. $75$ $m$
4. $15$ $m$

There is a printing mistake in the question, it should in cubic meter
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15 m

Step-by-step explanation:

Area required by one person = 6 sq.m.

Area required by 10 persons =

So, Area of base conical tent = 60 sq.m.

Formula of Area of base of cone  =

So,

Volume of cone =

=

Air required by 1 person = 30 cubic m

Air required by 10 person =

So, Volume of cone =

So,

Hence the height of the cone is approximately 15 m

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