devarshi-dt-logo

Question:

A gulab jamun contains sugar syrup up to about 30%

Solution:

Given:Radius(r)of cylindrical part=Radius(r)of hemispherical part =2.82=1.4 cmLength of each hemispherical part=Radius of hemispherical part=1.4 cmLength(h)of cylindrical part=5−2×length of hemispherical part→5−2×1.4=2.2 cmVolume of one gulab jamun=Volume of cylindrical part+ 2 ×Volume of hemispherical partWe know that, volume of a cylinder is πr²h and volume of a hemisphere is (2/3)πr³∴ Volume of one gulab jamun=πr²h+2×(2/3)πr³=πr²h+(4/3)πr³ →π×(1.4)²×2.2+(4/3)π(1.4)³ →(22/7)×1.4×1.4×2.2+(4/3)×(22/7)×1.4×1.4×1.4 [≈ π=22/7] →13.552+11.498=25.05 cm³Hence, volume of one gulab jamun=25.05 cm³So, volume of 45 gulab jamuns=45×25.05=1,127.25 cm³Also, given that, volume of sugar syrup=30%