Ex 12.2, 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 = (𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 )/2 = 2.8/2 = 1.4 cm
Here,
Diameter of hemisphere = 2.8 cm
Radius of hemisphere = (𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 )/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
Height of cylinder = 5 – 2 × 1.4
Height of cylinder = 5 – 2.8
Height of cylinder = 2.2 cm
Now,
Volume of cylinder = 𝜋𝑟2ℎ
= 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 πr3
= 𝟐/𝟑×𝟐𝟐/𝟕×(𝟏.𝟒)𝟑
= 2/3 × 22/7 × 1.4 × 1.4 × 1.4
= 5.75 cm3
Thus,
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 is 30%
So,
Syrup in 45 gulabjamun = 30% × 45 × 25.05
= 30/100 × 45 × 24.5
= 338.185 cm3
= 338 cm3 (approx)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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