A cloth having an area of `165` `m^(2)` is shaped into the form of a conical tent of radius `5` `m`.
(i) How many students can sit in the tent, if a student on an average occupies `(5)/(7)m^(2)` on the ground ?
(ii) Find the volume of the cone.

Explanation

(i) Number of student who can sit in the tent if a student, on an average, occupies `(5)/(7)m^(2)` on the ground
`=(pi r^(2))/((5)/(7))=(22)/(7)xx(5)^(2)xx(7)/(5)=110`.
(ii) Area of cloth `= 165 m^(2)`
Curved surface area of conical tent `= pi rl`
`therefore pi rl=165`
`rArr l=(165)/(pi)=(165)/((22)/(7)xx5)=(165xx7)/(22xx5)=(21)/(2)m`.
Now, `l^(2)=r^(2)+h^(2)`
`rArr h=sqrt(l^(2)-r^(2))=sqrt(((21)/(2))^(2)-(5)^(2))`
`rArr h=sqrt((441)/(4)-25)=(sqrt(341))/(2)`
`= (1)/(2)xx18.47=9.24m` (approx.)
Volume of conical tent `= (1)/(3)pi r^(2)h=(1)/(3)xx(22)/(7)xx(5)^(2)xx9.24`
`=(550xx9.24)/(21)=(5082)/(21)=242 m^(3)` .