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Question Number 29264 by bbbbbb last updated on 06/Feb/18

there are 25 persons in a conical tent every person needs an area of 4 sq m on the ground under the tent. if height if the tent is 18m.find the volume of the tent.

$$\mathrm{there}\:\mathrm{are}\:\mathrm{25}\:\mathrm{persons}\:\mathrm{in}\:\mathrm{a}\:\mathrm{conical}\:\mathrm{tent} \\ $$$$\mathrm{every}\:\mathrm{person}\:\mathrm{needs}\:\mathrm{an}\:\mathrm{area}\:\mathrm{of}\:\mathrm{4}\:\mathrm{sq}\:\mathrm{m}\: \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{under}\:\mathrm{the}\:\mathrm{tent}.\:\mathrm{if} \\ $$$$\mathrm{height}\:\mathrm{if}\:\mathrm{the}\:\mathrm{tent}\:\mathrm{is}\:\mathrm{18m}.\mathrm{find}\:\mathrm{the}\:\mathrm{volume} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{tent}. \\ $$

Answered by Rasheed.Sindhi last updated on 06/Feb/18

Total area of ground=4×25=100 sq m As the tent is conical so this ground is circle. If this circle has radius r πr^2 =100 Volume of the tent(V) of the height(h) V=(1/3)πr^2 h=(1/3)(πr^2 )h =(1/3)×100×18=600 m^3

$$\mathrm{Total}\:\mathrm{area}\:\mathrm{of}\:\mathrm{ground}=\mathrm{4}×\mathrm{25}=\mathrm{100}\:\mathrm{sq}\:\mathrm{m} \\ $$$$\mathrm{As}\:\mathrm{the}\:\mathrm{tent}\:\mathrm{is}\:\mathrm{conical}\:\mathrm{so}\:\mathrm{this}\:\mathrm{ground}\:\mathrm{is} \\ $$$$\mathrm{circle}.\:\mathrm{If}\:\mathrm{this}\:\mathrm{circle}\:\mathrm{has}\:\mathrm{radius}\:\mathrm{r} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\pi\mathrm{r}^{\mathrm{2}} =\mathrm{100} \\ $$$$\:\mathrm{Volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tent}\left(\mathrm{V}\right)\:\mathrm{of}\:\mathrm{the}\:\mathrm{height}\left(\mathrm{h}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{V}=\frac{\mathrm{1}}{\mathrm{3}}\pi\mathrm{r}^{\mathrm{2}} \mathrm{h}=\frac{\mathrm{1}}{\mathrm{3}}\left(\pi\mathrm{r}^{\mathrm{2}} \right)\mathrm{h} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{3}}×\mathrm{100}×\mathrm{18}=\mathrm{600}\:\mathrm{m}^{\mathrm{3}} \\ $$$$ \\ $$

Commented by bbbbbb last updated on 06/Feb/18

thank u

$$\mathrm{thank}\:\mathrm{u} \\ $$

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