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  • 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 Fig. 13.15).

3. 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 Fig).

                                             

Answers (1)

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It is clear from the figure that gulab jamun has one cylindrical part and two hemispherical parts.

Thus, the volume of gulab jamun is   =   Volume of cylindrical part  +  2 (Volume of the hemisphere )

Now, the volume of the cylinder is  =\ \pi r^2h

or                                         =\ \pi\times 1.4^2\times 2.2

or                                         =\ 13.55\ cm^3

And the volume of a hemisphere is  :

                                                       \\=\ \frac{2}{3}\pi r^3\\\\=\ \frac{2}{3}\times \pi \times (1.4)^3\\\\=\ 5.75\ cm^3                                             

Thus the volume of 1 gulab jamun is  = 13.55 + 2 (5.75) = 25.05 cm^3.

Hence the volume of 45 gulab jamun   =\ 45(25.05)\ cm^3\ =\ 1127.25\ cm^3

Further, it is given that one gulab jamun contains sugar syrup upto 30\% . 

So, the total volume of sugar present :

                                                         =\ \frac{30}{100}\times 1127.25\ =\ 338\ cm^3   

Posted by

Devendra Khairwa

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