Question

A circus tent is cylindrical upto a height of 3m and conical above it. If the diameter of base is 105 m and the slant height of conical part is 53 m, find the total canvas used in the tent.

Answer 1

Given

Circus tent = cylindrical up to height 3 m and conical above it.

Diameter of base =105 m ⇒ r = `105/2 = 52.5` m

Height of cylindrical part h = 3 m

Slant height of conical part l = 53 m

Take π = `22/7`

Total canvas used

Canvas area = CSA of cylinder + CSA of cone

1) Curved surface area of a cylinder

`CSA_"cyl" ​= 2πrh = 2 xx 22/7 xx 52.5 xx 3`

= `22/7 xx 105 xx 3`

= `22/7 xx 315`

= 22 × 45

= 990 m²

2) Curved surface area of a cone

`CSA_"cone​" = πrl`

= `22/7 xx 52.5 xx 53`

= `22/7 xx 105/2 xx 53`

= `(22 xx 105 xx 53)/14`

= `(11 xx 105 xx 53)/7`

= 11 × 15 × 53

= 8745 m²

3) Total canvas used

Total = 990 + 8745

= 9735 m²