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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. $15\;m$
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2 Answers

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Answer:

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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Answer is D.

Volume of a cone = (1/3)*pi*r^2*h

30 = 1/3*6*h where pi*r^2 = 6 m^2. On solving h, we will get h=15m

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