Last updated at Dec. 8, 2016 by Teachoo

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Ex 13.1,8 From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2. Since cylinder is solid, it has a base also whose area is also to be calculated. Total surface area of remaining solid = Curved Surface Area of cylinder + Area of cylinder base + Curved surface area of cone Curved Surface Area of cylinder Diameter = 1.4 cm So, radius = ๐ท๐๐๐๐๐ก๐๐/2 = 1.4/2 = 0.7 cm & Height = 2.4 cm Curved surface area of cylinder = 2๐๐โ = 2ร22/7ร(0.7)ร2.4 = 2ร22ร0.1ร2.4 = 10.56 cm2 Area of cylinder base Base of cylinder is a circle with radius = radius of cylinder = 0.7 cm So, Area of base = ๐๐2 = 22/7ร(0.7)2 = 22/7ร0.7ร0.7 = 22 ร0.1ร0.7 = 1.54 cm2 Curved Surface area of cone Curved Surface area of cone = ๐๐๐ Radius of cone = Radius of cylinder = 0.7 cm & Height of cone = h = 2.4 cm Now, we find slant height (l) We know that l2 = h2 + r2 l2 = (2.4)2 + (0.7)2 l2 = (2.4 ร 2.4 )2 + (0.7 ร 0.7)2 l2 = 5.76 + 0.49 l2 = 6.25 l = โ6.25 l = โ(625/100) l = โ((5 ร 5 ร 5 ร 5)/(10 ร 10)) l = (5 ร 5)/10 l = 25/10 l = 2.5 cm Curved surface area of cone = ๐๐๐ = 22/7ร0.7ร2.5 = 22ร0.1ร2.5 = 5.5 cm2 Hence, Total surface area of remaining solid = Curved Surface Area of cylinder + Area of cylinder base + curved surface area of cone = 10.56 + 1.54 + 5.5 = 17.6 cm2 Hence, area of remaining solid surface = 17.6 cm2 = 18 cm2 (approximately)

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