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Question
The height of a conical tent is 14 m and its floor area is 346.5 m2. How much canvas, 1.1 wide, will be required for it?
Options
490 m
525 m
665 m
860 m
Solution
525 m
Area of the floor of a conical tent= πr2
Therefore,
πr2 = 346.5
`=> 22/7xx"r"^2 = 346.5`
`=> "r"^2 =((3465)/10xx7/22)`
`=> "r"^2 = 441/4`
`=> "r"^2 = (21/2)^2`
`=> "r" = 21/2 "m"`
Height of the cone = 14 m
Slant height of the cone,`"l"=sqrt("r"^2 + "h"^2)`
`=sqrt((21/2)^2) + (14)^2`
`=sqrt(441/4) + 196`
`=sqrt(1224)/4`
`=35/4 "m"`
Area of the canvas = curved surface area of the conical tent
= πrl
`=(22/7xx21/2xx35/2)`
= 577.5 m2
`"Length of the canvas" ="Area of the canvas"/"width of the canvas"`
`= 577.5/1.1 "m"`
= 525 m
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