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.

From figure,

Diameter of gulab jamun (d) = 2.8 cm

Radius of cylindrical portion = Radius of hemispherical portion = r = $\dfrac{d}{2} = \dfrac{2.8}{2}$ = 1.4 cm.

Length of cylindrical portion (h) = 5 - 1.4 - 1.4 = 2.2 cm

Volume of each gulab jamun = Volume of cylindrical portion + 2 × Volume of each hemispherical portion

$= πr^2h + 2 \times \dfrac{2}{3}πr^3 \\[1em] = πr^2\Big(h + \dfrac{4}{3}r\Big) \\[1em] = \dfrac{22}{7} \times (1.4)^2 \times \Big(2.2 + \dfrac{4}{3} \times 1.4\Big) \\[1em] = 22 \times 0.2 \times 1.4 \times \Big(2.2 + \dfrac{5.6}{3}\Big) \\[1em] = 22 \times 0.2 \times 1.4 \times \dfrac{6.6 + 5.6}{3} \\[1em] = 22 \times 0.2 \times 1.4 \times \dfrac{12.2}{3} \\[1em] = \dfrac{75.152}{3} \\[1em] = 25.05 \text{ cm}^3.$

Volume of 45 gulab jamuns = 45 × 25.05 = 1127.28 cm³.

Given,

A gulab jamun, contains sugar syrup up to about 30% of its volume.

∴ Sugar syrup in 45 gulab jamuns = 30% of volume of 45 gulab jamuns

= $\dfrac{30}{100} \times 1127.28$ = 338.184 ≈ 338 cm³.

Hence, approximately 338 cm³ of sugar syrup would be found in 45 gulab jamuns.