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

Ex 13.2, 3 - Chapter 13 Class 10 Surface Areas and Volumes - Part 2
Ex 13.2, 3 - Chapter 13 Class 10 Surface Areas and Volumes - Part 3 Ex 13.2, 3 - Chapter 13 Class 10 Surface Areas and Volumes - Part 4 Ex 13.2, 3 - Chapter 13 Class 10 Surface Areas and Volumes - Part 5


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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 = ( )/2 = 2.8/2 = 1.4 cm Here, Diameter of hemisphere = 2.8 cm So, Radius of hemisphere = ( )/2 = 2.8/2 = 1.4 cm Now, Height of cylinder + 2 Radius of hemisphere = 5 cm Height of cylinder = 5 2 Radius of hemisphere = 5 2 1.4 = 5 2.8 = 2.2 cm Volume of cylinder = 2 = 22/7 (1.4)2 2.2 = 22/7 1.4 1.4 2.2 = 22 0.2 1.4 2.2 = 13.55 cm3 Volume of hemisphere Radius of hemisphere = 1.4 cm Volume of hemisphere = 2/3 r3 = 2/3 22/7 (1.4)3 = 2/3 22/7 1.4 1.4 1.4 = 5.75 cm3 Volume of 2 hemispheres = 2 Volume of hemisphere = 2 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 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% 45 25.05 = 30/100 45 24.5 = 338.185 cm3 = 338 cm3 (approx) So, syrup in 45 gulabjamun = 338 cm3 (approx)

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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.