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

Ex 13.1, 6 - Chapter 13 Class 10 Surface Areas and Volumes - Part 2
Ex 13.1, 6 - Chapter 13 Class 10 Surface Areas and Volumes - Part 3 Ex 13.1, 6 - Chapter 13 Class 10 Surface Areas and Volumes - Part 4


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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 = (𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 )/2 = 5/2 mm Here, Diameter of hemisphere = 5mm So, Radius of hemisphere = (𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 )/2 = 5/2 mm Now, Height of cylinder + 2 × Radius of hemisphere = 14 mm Height of cylinder = 14 – 2 × Radius of hemisphere = 14 – 2 × 5/2 = 14 – 5 = 9 mm Curved surface Area of cylinder = 2𝜋rh = 2×22/7×5/2×9 = (22 × 45)/7 = 990/7 mm2 Curved Surface area of hemisphere Radius of hemisphere = 5/2 mm Curved Surface Area of hemisphere = 2𝜋r2 = 2 ×22/7× (5/2)^2 = 2 ×22/7×(5 × 5)/(2 × 2) = (11 × 5 × 5)/7 = 275/7 mm2 Curved Surface area of 2 hemispheres = 2 × area of hemisphere = 2 × 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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.