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 hemsipherical ends with length 5 cm and diameter is 2.8 cm (see figure).


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

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