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.

Answer 1

Length of cylinder = 5 – 2.8 = 2.2 cm.
radius ,r = 1.4 cm
Volume of cylinder
$=\pi r^{2}h$
$=\pi \times {1.4}^2\times 2.2$
$=4.312\pi c{m}^2$
Volume of two hemispheres
$=2\times \left(\frac{2}{3}\pi r^3\right)$
$=\frac{4}{3}\pi \times {1.4}^3$
$=\frac{10.976}{3}\pi c{m}^2$
Total volume = Volume of two hemispheres + Volume of cylinder
$=4.312\pi +\frac{10.976}{3}\pi$
Volume of syrup = 30% of total volume
$=\pi (4.312+\frac{10.976}{3})\times 30\%$
$=\frac{23.912}{3}\times \frac{30}{300}\times \frac{22}{7}$
$=7.515c{m}^3$
Volume of syrup in 45 gulab jamuns $=45\times 7.515=338.184c{m}^3$