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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 5 cm and diameter 2.8 cm (see the given figure). [Use \(\pi=\frac{22}{ 7}\)]
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 5 cm and diameter 2.8 cm (see the given figure). [Use \(\pi=\frac{22}{ 7}\)]
Updated On: Jan 13, 2026
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Solution and Explanation
The radius (r) of both the cylindrical and hemispherical parts is \(\frac{2.8}{2}=1.4\) cm. The length of each hemispherical part is equal to its radius, which is 1.4 cm. The length (h) of the cylindrical part is calculated as 5 − 2 × 1.4 = 2.2 cm.
The volume of a single gulab jamun is the sum of the volume of the cylindrical part and twice the volume of a hemispherical part, expressed as \( \pi r^2h+ 2 × (\frac{2}{3})\pi r^3 \).
\(= 4.312\pi +(\frac{10.976}{3}) \pi\) = 25.05 cm3.
The total volume of 45 gulab jamuns is 45 × 25.05 = 1,127.25 cm3.
The volume of sugar syrup is 30% of the total volume, calculated as 45 × 30% (25.05 cm3) = 45 × 7.515 = 338.184 cm3.
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