A colth having an area of `165 m^(2)`is shapped 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.

Answer

(i) 110 (ii) `241.7 m^(3)`

Explanation

(i) Area of the floor of the tent `= pir^(2) = ((22)/(7) xx 5 xx 5) m^(2)`
Area occupied by each student `= (5)/(7) m^(2)`
Required number of student `(((22)/(7) xx 5 xx 5))/(((5)/(7))) = 110`
(ii) Curved surface area of the tent = area of cloth `= 165 m^(2)`
`pirl 165 rArr (22)/(7) xx 5 xx l = 165 rArr l = ((165 xx 7)/(22 xx 5)) m = (21)/(2)m`
`h^(2) = (l^(2) - r^(2)) = {((21)/(2))^(2) - 5^(2)} = (341)/(4) = 85.25`
`:. h = sqrt(85.25) = 9.25 m`
Volume of the tent `= (1)/(3) pir^(2) h = ((1)/(3) xx (22)/(7) xx 5 xx 5 xx 9.23) m^(3) = 241.7 m^(3)`