Question

A circus tent is cylindrical to a height of $$3$$ metres and conical above it. If its diameter is $$105$$ m and the slant height of the conical portion is $$53$$ m, calculate the length of the canvas $$5$$ m wide to make the required tent.

Answer 1

For cylindrical part, we have

$$h=$$Height$$=3$$m, $$r=$$radius$$=\dfrac{105}{2}$$m

For conical part, we have

$$l_1=$$Slant height$$=53$$m, $$r_1=$$radius of base$$=\dfrac{105}{2}$$m$$=r$$

$$\therefore$$ Total curved surface area$$=2\pi rh+\pi rl$$

$$=\pi r(2h+l)=\dfrac{22}{7}\times \dfrac{105}{2}\times (6+53)m^2=11\times 15\times 59m^2$$

Hence, length of $$5$$m wide canvas$$=\dfrac{11\times 15\times 59}{5}$$m

$$=1947$$m.