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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 cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm. [4 MARKS]

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Solution

Concept: 1 Mark
Application: 3 Marks

Each gulab jamun has shape of cylinder with two hemispherical ends.


Diameter of Cylinder = Diameter of 2 Hemispheres
=d=2.8 cm

Radius of Cylinder = Radius of 2 Hemispheres
=r=2.82=1.4 cm

Height of Cylinder =h=51.41.4=2.2 cm

Volume of 1 gulab jamun = volume of cylinder + volume of 2 hemispheres

=πr2.h+23.π.r3+23.π.r3

=r2.π.(h+23.r+23.r)=πr2(h+43.r)

Volume of 45 gulab jamuns
=45×π.r2(h+43.r)

Volume of Syrup
=30100×45×π.r2(h+43.r)

=30100×45×227×1.4×1.4(2.2+43×1.4)

=310×45×227×1.4×1.4(4.067)

=338.184 cm3


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