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Answer :
Volume of the gulab jamun = Volume of the cylindrical portion + Volume of the hemispherical ends
\( = \ \pi r^2 h \ + \ 2( \frac{2}{3} \pi r^3) \ \)
\( = \ \pi r^2 (h \ + \ \frac{4}{3} r) \)
where r = 1.4 cm, h = 2.2 cm
\( = \ \frac{22}{7} \ × \ (1.4)^2 \ × \ (2.2 \ + \ \frac{4}{3} \ × \ 1.4) \ \)
\( = \ \frac{22}{7} \ × \ 1.96 \ × \ ( \frac{6.6 \ + \ 5.6}{3} ) \)
\( = \ \frac{22}{7} \ × \ 1.96 \ × \ \frac{12.2}{3} \) cm3
Volume of 45 gulab jamuns
\( = \ 45 \ × \ \frac{22}{7} \ × \ 1.96 \ × \ \frac{12.2}{3} \) cm3
Quantity of syrup in gulab jamuns = 30% of their volume
\( = \ \frac{30}{100} \ × \ 45 \ × \ \frac{22}{7} \ × \ 1.96 \ × \ \frac{12.2}{3} \)
\(= \ \frac{9 \ × \ 11 \ × \ 1.96 \ × \ 12.2}{7} \ \)
\( = \ 338.184 \)
\(= \ 338 \) cm3