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Ex 13.1, 6 - A medicine capsule is in shape of a cylinder - Ex 13.1

  1. Chapter 13 Class 10 Surface Areas and Volumes
  2. Serial order wise
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Ex 13.1, 6 A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area. Total area of the capsule = Curved Surface area of cylinder + Curved Surface area of 2 hemispheres Curved Surface area of cylinder Diameter of cylinder = 5 mm Radius of cylinder = (๐ท๐‘–๐‘Ž๐‘š๐‘’๐‘ก๐‘’๐‘Ÿ )/2 = 5/2 mm Here, Diameter of hemisphere = 5mm So, Radius of hemisphere = (๐ท๐‘–๐‘Ž๐‘š๐‘’๐‘ก๐‘’๐‘Ÿ )/2 = 5/2 mm Now, Height of cylinder + 2 ร— Radius of hemisphere = 14 mm Height of cylinder = 14 โ€“ 2 ร— Radius of hemisphere = 14 โ€“ 2 ร— 5/2 = 14 โ€“ 5 = 9 mm Curved surface Area of cylinder = 2๐œ‹rh = 2ร—22/7ร—5/2ร—9 = (22 ร— 45)/7 = 990/7 mm2 Curved Surface area of hemisphere Radius of hemisphere = 5/2 mm Curved Surface Area of hemisphere = 2๐œ‹r2 = 2 ร—22/7ร— (5/2)^2 = 2 ร—22/7ร—(5 ร— 5)/(2 ร— 2) = (11 ร— 5 ร— 5)/7 = 275/7 mm2 Curved Surface area of 2 hemispheres = 2 ร— area of hemisphere = 2 ร— 275/7 = 550/7 mm2 Total area of the capsule = Curved Surface area of cylinder + Curved Surface area of 2 hemispheres = 990/7+550/7 = (990 + 550)/7 = 1540/7 = 220 mm2 Hence, Total surface area of capsule = 220 mm2

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