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

Answer 1

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