Question

A military tent of height 8.25 m is in the form of a right circular cylinder of base diameter 30 m and height 5.5 m surmounted by a right circular cone of same base radius. Find the length of canvas used in making the tent, if the breadth of the canvas is 1.5 m.

Answer 1

We have,
the radii of bases of the cone and cylinder, r = 15 m,
the height of the cylinder, h = 5.5 m,
the height of the tent = 8.25 m
Also, the height of the cone, H = 8.25 - 5.5 = 2.75 m

The slant height of the cone, l = `sqrt(r^2 + H^2)`

`= sqrt(15^2 + 2.75^2)`

`= sqrt(225 + 7.5625)`

`= sqrt(232.5625)`

`= 15.25` m

The area of the canvas used in making the tent = CSA of cylinder + CSA  of cone 

= 2πrh + πrl

=  πr(2h + l)

`= 22/7 xx15 (2xx5.5+15.25)`

`=22/7xx 15(11 + 15.25)`

`=22/7 xx15xx26.25`

= 1237.5  m²

As, the width of the canvas = 1.5 m

So, the length of the canvas =`237.5/1.5 = 825` m  

Hence, the length of the tent used for making the tent is 825 m.