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प्रश्न
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).
उत्तर
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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Match the column:
| (1) surface area of cuboid | (A) πr2h |
| (2) surface area of closed right cylinder | (B) 2πr(h + r) |
| (3) Total surface area of right cone | (C) πrl + πr2 |
| (4) Total surface area of hemisphere | (D) 3πr3 |
| (E) 3πr2 | |
| (F) 2[lb + bh + lh] |
