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]
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=5−1.4−1.4=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