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An oil funnel of tin sheet consists o...

An oil funnel of tin sheet consists of a cylindrical portion 10 cm long attached to a frustum of a cone. If the total height be 22 cm, the diameter of the cylindrical portion 8 cm and the diameter of the top of the funnel 18 cm, find the area of the tin required. (Use `pi=22//7` )

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Given oil funnel is combination of a cylinder and a frustum of a cone .
Also given height of cylinder portion h=10cm
and , radius `r_(2)=(8)/(2)=4cm`
Diameter of top of the funnel =18 cm
Radius of top of the funnel `r_(1)=(18)/(2)=9 cm `
Now height of the frustum of cone =22-10=12 cm
Slant height of he frustum l=`sqrt((12)^(2)(9-4)(2))`
`=sqrt(144+25)=sqrt(169)`
l=13 cm
Required area of the tin sheet =curved surface area of cylinder portion +curved surface area of the frustum
`=2pir_(2)h+pi(r_(1)+r_(2))l=(22)/(7)[2xx4xx10+(9+4)13]`
`=(22)/(7)(80+169)=(22)/(7)xx249=(5478)/(7)=782(4)/(7) cm^(2)`
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