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. [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 3 Marks

Each gulab jamun has shape of cylinder with two hemispherical ends.

Diameter of Cylinder = Diameter of 2 Hemispheres
$=d=2.8cm$

Radius of Cylinder = Radius of 2 Hemispheres
$=r=\frac{2.8}{2}=1.4cm$

Height of Cylinder $=h=5-1.4-1.4=2.2cm$

Volume of 1 gulab jamun = volume of cylinder + volume of 2 hemispheres

$=\pi r^2.h+\frac{2}{3}.\pi .r^3+\frac{2}{3}.\pi .r^3$

$=r^2.\pi .(h+\frac{2}{3}.r+\frac{2}{3}.r)=\pi r^2(h+\frac{4}{3}.r)$

Volume of 45 gulab jamuns
$=45\times \pi .r^2(h+\frac{4}{3}.r)$

Volume of Syrup
$=\frac{30}{100}\times 45\times \pi .r^2(h+\frac{4}{3}.r)$

$=\frac{30}{100}\times 45\times \frac{22}{7}\times 1.4\times 1.4(2.2+\frac{4}{3}\times 1.4)$

$=\frac{3}{10}\times 45\times \frac{22}{7}\times 1.4\times 1.4\left(4.067\right)$

$=338.184c{m}^3$