Question

A gulab jamun contains sugar syrup upto 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 5cm and diameter 2.8cm
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Answer 1

Step-by-step explanation:

Volume of gulab jamun = volume of cylinder ( present in the central portion ) and the volume of the two spheres present at the peripheral ends .

Find the volume of the gulab jamun

Volume of cylinder

Diameter = 2.8 cm

⇒ radius = diameter / 2

⇒ radius = 2.8 cm / 2

⇒ radius = 1.4 cm

Height of the gulab jamun = 5 cm - 2.8 cm

⇒ 2.2 cm

Volume =  π r² h

⇒ 22/7 × ( 1.4 )² × 2.2

⇒ 22/7 × 1.4 × 1.4 × 2.2

⇒ 22 × 0.2 × 1.4 × 2.2

⇒ 4.4 × 1.4 × 2.2

⇒ 13.55 cm³

Volume of 2 hemispheres

Volume = 2 × 2/3 π r³

⇒ 4/3 × 22/7 × ( 1.4 )³

⇒ 4/3 × 22/7 × 1.4 × 1.4 × 1.4

⇒ 4/3 × 22 × 0.2 × 1.4 × 1.4

⇒ 11.5 cm³

Volume of each gulab jamun

Volume = 13.55 + 11.5

⇒ 25.05 cm³

Volume of 45 ones

Volume = 45 × 25.05

⇒ 1127.25

Volume of syrup

Volume = 30 % of 1127.25

⇒ 30/100 × 1127.25

⇒ 1127.25 × 0.3

⇒ 338.175

The volume of syrup is 338.175 cm³ .