Question

A 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 the given figure). [Use $\pi=\frac{22}{ 7}$]

Answer 1

It can be observed that
Radius (r) of cylindrical part = Radius (r) of hemispherical part = $\frac{2.8}{2}=1.4$ cm
Length of each hemispherical part = Radius of hemispherical part = 1.4 cm
Length (h) of cylindrical part = 5 − 2 × Length of hemispherical part = 5 − 2 × 1.4 = 2.2 cm

Volume of one gulab jamun = Vol. of cylindrical part + 2 × Vol. of hemispherical part
$= \pi r^2h+ 2 × (\frac{2}{3})\pi r^3$

$= 4.312\pi +(\frac{10.976}{3}) \pi$
= 25.05 cm3

Volume of 45 gulab jamuns = 45×25.05 = 1,127.25 cm3

Volume of sugar syrup = 30% of volume
= 45×30% (25.05 cm3)
= 45×7.515 = 338.184 cm3