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Five persons can accommodate in a conica...

Five persons can accommodate in a conical tent. If each person required `18` square decimetre place on wrath and `108` cubic decimetre air for breathing, then find the height of the cone.

Text Solution

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Area required for `1` person on floor `= 18` `"decimetre"^(2)`
Area required for `5` persons on floor `=5xx18=90"decimetre"^(2)`
`therefore pi r^(2)=90`
Similarly, air required for 1 person `= 108 "decimetre"^(3)`
`therefore` Air required for 5 persons `=5xx108=540 "decimetre"^(3)`
`rArr (1)/(3)pi r^(2)h=540`
`rArr (1)/(3)xx90xx h=540`
`rArr h=(540)/(30)=18` decimetre
`therefore` Height of tent `= 18` decimetre
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