A circus tent is cylindrical to a height of 3 cm and conical above it. If its base radius is 52.5 m and the slant height of the conical portion is 53 m, find the area of canvas needed to make the tent. [Take π = 22/7.]
Total area of canvas required = CSA of cylindrical part + CSA of conical part [CSA = Curved surface area]
Now,
Radius of cone = Radius of cylinder = r = 52.5 m
Height of cylindrical part, h = 3 cm = 0.03 m [As 1 m = 100 cm]
Lateral height of conical part, l = 53 m
Now, we know
CSA of cylinder = 2πrh
Where, r is base radius and h is height of cylinder and
CSA of cone = πrl
Where, r is base radius and l is slant height.
Area of canvas required = 2πrh + πrl
= πr(2h + l)
= 8754.9 m2