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 5 cm and diameter 2.8 cm (see figure). For one gulab jamun, 

Answer 1

For each gulab jamun:

Diameter = 2.8 cm ⇒ r = 1.4 cm

Total length = 5 cm

Cylindrical length h = 5 − 2r =

5 − 2(1.4)

= 2.2 cm

Volume of one gulab jamun (capsule shape)

V = `πr^2h + 4/3πr^3`

= `π (1.4)^2 (2.2) + 4/3 π(1.4)^3`

= `π(1.96)(2.2) + 4/3 π (2.744)`

= π(4.312 + 3.659) ≈ π(7.971) ≈ 25.05 cm³

Volume of 45 gulab jamuns

45 × 25.05 ≈ 1127.25 cm³

Syrup is 30% of volume:

0.30 × 1127.25

= 338.18 cm³