Q. 103.8( 13 Votes )

A gulab - jamun contain 40% sugar syrup in it. Find how much syrup would be there in 50 gulab - jamuns, each shaped like a cylinder with two hemispherical ends with total length 5 cm and diameter 2.8 cm.

Answer :

Given.


40% of sugar syrup in 1 gulab - jamun


Having length is 5 cm


And diameter is 2.8 cm


Formula used/Theory.


Volume of cylinder = πr2h


Volume of hemisphere = πr3


If gulab - jamun shape like cylinder between 2 hemisphere


Volume of gulab - jamun = volume of cylinder


+ 2 × Volume of hemisphere


Diameter of hemisphere = 2.8 cm


Radius of hemisphere = = 1.4 cm


Height of cylinder = length of gulab - jamun–2 × radius


= 5 cm–2 × 1.4


= 5 cm – 2.8 cm


= 2.2 cm


Volume of gulab - jamun = volume of cylinder


+ 2 × Volume of hemisphere


= πr2h + 2 × πr3


= πr2[h + r]


= × 1.4 × 1.4 × [2.2 + × 1.4]


= 22 × 0.2 × 1.4 × [2.2 + 1.86]


= 22 × 0.2 × 1.4 × [4.06]


= 25.0096 cm3


Volume of sugar syrup = × 25.0096 cm3


Volume of sugar syrup = 10.0038 cm3


Volume of sugar syrup in 50 gulab - jamun = 50 × 10.0038 cm3


= 500.192 cm3


1 cm3 = litres


500.192 cm3 = litres


= 0.500192 litres


= 0.5 litres (approx.)


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