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A gulab jamun contains, sugar syrup upto about $30 %$ of its volume. What is the approximate amount of syrup to 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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338.000 cm 3

338.25 cm 3

228.175 cm 3

338.885 cm 3

answer is B.

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Detailed Solution

Given that the amount of sugar syrup is 30%, the numbers of gulab jamuns are 45, the length is 5cm and its diameter is 2.8cm.
Question Image

Radius of gulab jamun = 2.8/2 = 1.4 cm
We have the following formulae,
Volume of cylinder

= π r 2 h

Volume of hemisphere

= 23 π r 3

Volume of gulabjamun = Volume of cylinder

+ 2 ×

volume of hemisphere

= π r 2 h + 2 × 23 π r 3 = π r 2 h + 4 r 3

= 227 × 1.4 × 1.4 2.2 + 4 × 1.4 3

= 22 × 0.2 × 1.4 (2.2 + 1.866) = 25.05 cm 3

Volume of 45 gulab jamuns will be,

= 45 × 25.05 = 1127.34 cm 3

Percentage of syrup

30 %

Therefore, the sugar syrup present in 45 gulab jamuns,

= 1127.34 × 0.3 = 338.25 cm 3

Thus 45 gulab jamuns have

338.25 cm 3

syrup.
Therefore the correct option is 2.

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