Question

A Gulab Jamun when completely ready for eating contains sugar syrup up to about $30\%$ of its volume. Find approximately how much syrup would be found in $45$ Gulab Jamun shaped like a cylinder with two hemispherical ends, if the complete length of each of the Gulab Jamun is $5cm$ and its diameter is $2.8cm$.

Answer 1

Given:
Diameter of the hemispherical end of Gulab Jamun is $2.8cm$
Therefore its radius will be $\frac{2.8}{2}=1.4cm$
Here, each Gulab Jamun is in the shape of a cylinder with 2 hemispherical ends
And the total height of the Gulab Jamun $=5cm$ [given]
So the height of the cylindrical part of the Gulab Jamun $=5-2\times \left(1.4\right)=2.2cm$
$\therefore$ The volume of 1 Gulab Jamon $=\frac{2}{3}\pi r^3+\pi r^{2}h+\frac{2}{3}\pi r^3$

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

$=\frac{22}{7}\times {\left(1.4\right)}^2(2.2+\frac{4}{3}\times 1.4)$

$=25.05c{m}^3$

Therefore, the volume of $45$ Gulab jamuns $=45\times 25.05c{m}^3$

Given: Volume of syrup in each Gulab Jamun $=30\%$ of its volume.
$\therefore$ Volume of syrup in $45$ gulabjamoons $=\frac{30}{100}\times 45\times 25.05$

$=338.176c{m}^3$