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Surface Areas and Volumes
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02/07/2021 10:54 am
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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 Fig.).
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02/07/2021 10:58 am
Diameter of upper circular end of frustum part = 18 cm
Radius (r1) = 9 cm
r2 = 8/2 = 4 cm
Now, height (h1) of the frustum section = 22 – 10 = 12 cm
Height (h2) of cylindrical section = 10 cm (given)
Now, the slant height will be
l = \(\sqrt{(r_1 - r_2)^2 + h_1^2}\)
l = 13 cm
Area of tin sheet required = CSA of frustum part + CSA of cylindrical part
= π(r1 + r2)l + 2πr2h2
Solving this we get,
Area of tin sheet required = 782 × (4/7) cm2