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 the canvas used in making the tent, if the breadth of the canvas is 1.5 m.

Answer 1

It is given that, radius of cylinder `(r_1)=30/2m=15m`

Height of cylinder (h₁) = 5.5 m

And, height of the tent (H) = 8.25 m

So, height of cone (h₂) = 8.25 m − 5.50 m = 2.75 m

And, radius of cone (r₂) = 15 m

Let the slant height of the cone be l m.

`therefore l^2=(15m)^2+(2.75m)^2`

`rArr l^2=(225+7.5625)m^2`

`rArr l=sqrt232.5625m`

`rArrl=15.25 m`

Curved surface area of the tent = Curved surface area of cylinder + Curved surface area

of cone

`=2pir_1h_1+pir_2l`

`=(2xx22/7xx15xx5.5)cm^2+22/7xx15xx15.25cm^2`

`=(518.57+718.93)cm^2`

`=1237.5m^2`

Now, curved surface area of the tent is equal to the area of rectangular piece of canvas.

It is given that, breadth of canvas = 1.5 m

Let l be the length of canvas.

∴l × 1.5 = 1237.5

`rArrl=1237.5/1.5=825m`

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