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 $5cm$ and diameter $2.8cm$.

Answer 1

Total volume of gulabjamun $=\pi r^{2}h+2\times \frac{2}{3}\pi r^3$

Total volume of $45$ gulabjamuns

V.of cyl= $\pi r^{2}h$

V. of hemisphere $=\frac{2}{3}\pi r^3$

$=45\times$ volume of $1$ gulabjamun

$=45\times (\pi r^{2}h+\frac{4}{3}\pi r^3)=45\times (\pi {\left(\frac{d}{2}\right)}^{2}h+\frac{4}{3}\pi {\left(\frac{d}{2}\right)}^3)$

$=45\times \pi \left(\right(1.4{)}^2\times 5+\frac{4}{3}\left(1.4{)}^3\right)=1902.67c{m}^3$

A gulabjamun syrup percentage $=30\%$ of its volume

Total syrup $=30\%$ ot total volume $=\frac{30}{100}\times 1902.67$

$=570.80c{m}^2$