Question

Find the area of canvas required for a conical tent of height 24 m and base radius 7 m.

Answer 1

The area of canvas required to make a conical tent of height 24 m and base radius 7 m is 550 m².

• Given,

Height of the conical tent (h) = 24 m

Base radius of the conical tent (r) = 7 m

• Slant height of the conical tent (l) = √(h² + r²)   [Refer to the image attached below]

Or, l = √{ (24 m)² + (7 m)² }

Or, l = √( 576 m² + 49 m²)

Or, l = √625 m²

Or, l = 25 m

Therefore, slant height of the tent is 25 m.

• Now, area of canvas required for the tent = Curved surface area of the tent

Curved surface of the tent (C.S.A.) = Curved surface area of a cone

 

• Now, the curved surface area of a cone is given as πrl.

Therefore,

C.S.A. = πrl  

Or, C.S.A. = (22 / 7) × 7 m × 25 m

Or, C.S.A. = (22 × 7 m × 25 m) / 7

Or, C.S.A. = 22 × 1 m × 25 m

Or, C.S.A. = 550 m²

∴  Area of canvas required to make the tent = 550 m²