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)

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   

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