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 = πr^{2}h

Volume of hemisphere = πr^{3}

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

= πr^{2}h + 2 × πr^{3}

= πr^{2}[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 cm^{3}

Volume of sugar syrup = × 25.0096 cm^{3}

Volume of sugar syrup = 10.0038 cm^{3}

Volume of sugar syrup in 50 gulab - jamun = 50 × 10.0038 cm^{3}

= 500.192 cm^{3}

1 cm^{3} = litres

500.192 cm^{3} = litres

= 0.500192 litres

= 0.5 litres (approx.)

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