In chapter surface areas and volume of ncert class 10 give me the solution of exercise 13.1 question number 3 . Find the best solution of the question , also give me the simplest method of this 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 (see figure)
It is known that the gulab jamuns are similar to a cylinder with two hemispherical ends.
So, the 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