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Ex 13.2, 3 - Gulab jamun, contains sugar syrup up to about 30 - Ex 13.2

  1. Chapter 13 Class 10 Surface Areas and Volumes
  2. Serial order wise
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Ex 13.2, 3 Gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm (see figure) Lets first find volume of 1 gulab jamun Since gulabjamun contains one cylinder and 2 hemispheres Volume of gulab jamun = Volume of cylinder + Volume of 2 hemispheres Volume of cylinder Diameter of cylinder = 2.8 cm Radius of cylinder = (๐ท๐‘–๐‘Ž๐‘š๐‘’๐‘ก๐‘’๐‘Ÿ )/2 = 2.8/2 = 1.4 cm Here, Diameter of hemisphere = 2.8 cm So, Radius of hemisphere = (๐ท๐‘–๐‘Ž๐‘š๐‘’๐‘ก๐‘’๐‘Ÿ )/2 = 2.8/2 = 1.4 cm Now, Height of cylinder + 2 ร— Radius of hemisphere = 5 cm Height of cylinder = 5 โ€“ 2 ร— Radius of hemisphere = 5 โ€“ 2 ร— 1.4 = 5 โ€“ 2.8 = 2.2 cm Volume of cylinder = ๐œ‹๐‘Ÿ2โ„Ž = 22/7ร—(1.4)2ร—2.2 = 22/7ร—1.4ร—1.4ร—2.2 = 22ร—0.2ร—1.4 ร— 2.2 = 13.55 cm3 Volume of hemisphere Radius of hemisphere = 1.4 cm Volume of hemisphere = 2/3 ฯ€r3 = 2/3ร—22/7ร—(1.4)3 = 2/3ร—22/7ร—1.4ร—1.4ร—1.4 = 5.75 cm3 Volume of 2 hemispheres = 2 ร— Volume of hemisphere = 2 ร— 5.75 = 11.50 cm3 Now, Volume of gulab jamun = Volume of cylinder + Volume of 2 hemispheres = 13.55 + 11.50 = 25.05 cm3 So, volume of 1 gulabjamun = 25.05 cm3 Volume of 45 gulabjamun = 45 ร— 25.05 cm3 We need to find quantity of syrup in 45 gulabjamun It is given that quantity of syrup in gulabjamun = 30% So, syrup in 45 gulabjamun = 30% ร— 45 ร— 25.05 = 30/100 ร— 45 ร— 24.5 = 338.185 cm3 = 338 cm3 (approx) So, syrup in 45 gulabjamun = 338 cm3 (approx)

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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