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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 $$5 \ cm$$ and its diameter is $$2.8 \ cm$$.


Solution

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

                                                        $$=\pi r^2\left ( h+\dfrac{4}{3}r \right )$$

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

                                                       $$=25.05\ cm^3$$

Therefore, the volume of $$45$$ Gulab jamuns $$ = 45 \times 25.05 \ cm^3$$

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

                                                                  $$=338.176 \ cm^3$$

Mathematics

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