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  1. Chapter 13 Class 10 Surface Areas and Volumes
  2. Serial order wise
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Ex 13.5, 5 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. 13.25) Area of tin sheet = CSA of Cylinder + CSA of frustum of cone Cylinder Radius of cylinder = 8/2 = 4cm Height of cylinder = 10cm CSA = 2๐œ‹๐‘Ÿโ„Ž = 2๐œ‹ ร— (8/2) ร— 10 = 2๐œ‹ ร— (4) ร— 10 = 80 ๐œ‹ ๐‘๐‘š^2 Frustum of cone Height of frustum = 22cm โˆ’ 10cm = 12cm ๐‘Ÿ_1=18/2 = 9cm ๐‘Ÿ_2=8/2 = 4cm CSA = ฯ€(๐‘Ÿ_1+ ๐‘Ÿ_2 )๐‘™ Slant height, l =โˆš(โ„Ž^2+(๐‘Ÿ_1 โˆ’๐‘Ÿ_2 )^2 ) l =โˆš((22 โˆ’10)^2+(18/2โˆ’8/2)^2 ) l = โˆš((12)^2+(9โˆ’4)^2 ) = โˆš((12)^2+(5)^2 ) = โˆš(144 +25) = โˆš169 = 13cm Thus, CSA = ฯ€(๐‘Ÿ_1+ ๐‘Ÿ_2 )๐‘™ = ๐œ‹ ร— 13 ร— (18/2+8/2) = ๐œ‹ ร— 13 ร— (9 + 4) = ๐œ‹ ร— 13 ร— 13 = 169 ๐œ‹ ๐‘๐‘š^2 โˆด Area of tin sheet = 80๐œ‹ + 169๐œ‹ = 249๐œ‹ ๐‘๐‘š^2 = 249 ร— 3.14 ๐‘๐‘š^2 = 781.86 ๐‘๐‘š^2

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