Question

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 cylindrical with two hemispherical ends with length 5 cm and diameter 2.8 cm.

Answer 1

In one gulab jamun ;

Height = h = 5 cm
Radius = 2.8/2 = 1.4 cm

Volume of each gulab jamun
= volume of a cylinder + volume of two hemisphere
= πr^2h + (2/3)πr^3 + (2/3)πr^3
= πr^2h + (4/3)πr^3
= π × (r^2h+r^3)
= (22/7) × [(1.4×1.4×5) + (1.4×1.4×1.4)]
= (22/7) × (9.8+2.744)

= 39.424 cubic cm
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Volume of syrup in one gulab jamun
= 30% of 39.424
= (30/100) × 39.424
= 11.8272 cubic cm
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Amount of syrup in 45 gulab jamuns
= 45 × 11.8272
= 532.224 cubic cm
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