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Question
An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel (see the given figure).
Solution
Radius (r1) of upper circular end of frustum part = 18/2 = 9 cm
Radius (r2) of lower circular end of frustum part = Radius of circular end of cylindrical part
= 8/2 = 4 cm
Height (h1) of frustum part = 22 − 10 = 12 cm
Height (h2) of cylindrical part = 10 cm
Slant height (l) of frustum part =
` sqrt(r_1-r_2^2+h_2) = sqrt((9-4)^2+(12)^2) = 13 cm`
Area of tin sheet required = CSA of frustum part + CSA of cylindrical part
`=pi(r_1+r_2)l+2pir_2h_2`
`=22/7xx(9+4)xx13+22/7xx4xx10`
`=22/7[169+80] = (22xx249)/7`
`=782 4/7 cm^2`
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