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
Answers
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 .