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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.
Solution
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.
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