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Surface Areas and Volumes
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27/06/2021 12:42 pm
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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 figure).
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27/06/2021 12:44 pm
Total height of a gulab jamun = 5 cm.
Diameter = 2.8 cm
So, radius = 1.4 cm
∴ The height of the cylindrical part = 5 cm – (1.4 + 1.4) cm
= 2.2 cm
Now, total volume of One Gulab Jamun = Volume of Cylinder + Volume of two hemispheres
= πr2h + (4/3)πr3
= 4.312π + (10.976/3) π
= 25.05 cm3
We know that the volume of sugar syrup = 30% of total volume
So, volume of sugar syrup in 45 gulab jamuns = 45 × 30(25.05 cm3)
= 45 × 7.515
= 338.184 cm3