The height of the conical tent is 14m and its floor area is 346.5m2. How much canvas, 1.1m wide, will be required for it
Given: The height of the conical tent is 14m and its floor area is 346.5m2.
Canvas of width 1.1m
Surface area of the tent is: πrl
Let be the Surface area of the cone.
Area of the floor is : πr2= 346.5 m2
⇒ πr2= 346.5
⇒ r2 = =
⇒ r = √( ) =
⇒ l = √(h2 + r2) (here l is the slant height and h , r are height and radius respectively of cone)
⇒ l = √(142 + ()2) = √(196 +
) = √
=
∴ S = πrl = π × =
∴ Area of the canvas required to cover the tent is: m2
∴ l × b = m2 (here l is length and b is breadth or width of the canvas)
⇒ l × 1.1 = ( width of the canvas is 1.1m)
⇒ l = = 525m
∴ Length of the canvas required to cover the tent is 525m