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In a right circular conical tent 11 pers...

In a right circular conical tent 11 persons can stay. For each person 4 sq-m space in the base and `20 m^3` air are neccessary. Determine the height of the tent put up exactly for 11 persons.

Text Solution

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Let the radius of the base of the ent be r metre.
`therefore` the area of the base `=pi r^2` sq-metre.
Again , space required for staying for 11 persons `=11xx4` sq -m . `=44` sq-m.
`therefore (22)/(7)xxr^2=44rArr r^2=14`.
Again , the total air required for 11 person `=20xx11 m^3=220m^3`.
Now , if the height of the tent be h metre, then its volume `=(1)/(3)pi r^2h` cubic - metres. As per questions , `(1)/(3)xx(22)/(7)xx r^2h=220`.
`or ,(1)/(3)xx(22)/(7)xx14xxh=220 [because r^2=14] or , h=(220xx3xx7)/(22xx14) or , h=15`
Hence , the height of the tent = 15 metres.
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