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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. |
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Answer» (i) Given, radius of the base of conical tent = 5 m and area needs to sit a student on the ground `= (5)/(7)m^(2)` `therefore` Area of the base of a conical tent `= pir^(2)`. `= (22)/(7) xx 5 xx 5m^(2)` Now, number of students `= ("Area of the bases of a conical tent")/("Area needs to sit a student on the groud")` `= ((22xx5xx5)/(7))/(5//7) = (22)/(7) xx 5 xx 5xx(7)/(5) = 110` Hence, 110 students can sit in the conical tent . (ii) Given, area of the form a conical tent `= 165m^(2)` Radius of the base of a conical tent , r = 5 m Curved surface area of the = Area of cloth to from a conical tent `rArr" "pirl = 165` `rArr" "(22)/(7)xx (5) xx l = 165` `therefore" " l = (165 xx 7)/(22 xx5) = (33xx7)/(22) = 10.5m` Now, height of a conical tent = `sqrt(l^(2) - r^(2)) = sqrt((10.5)^(5) - (5)^(2))` ` = sqrt(110.25 - 25 ) = sqrt(8528) = 9.23m` Volume of a cone (conical tent) `=(1)/(3) pir^(2)h = (1)/(3) xx (22)/(7) xx 5 xx 5 xx 923` ` = (1)/(3) x (1550xx 923)/(7) = (50765)/(7xx3) = 241.7m^(3)` Hence, the volume of the (conical tent ) is `241.7m^(3)` |
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