Question

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).​

Answer 1

$\huge{\bf{\underline{\boxed{\mathfrak{\green{Solution:-}}}}}}$

Here,

Diameter = 2.8 cm

So, radius of cylinder = radius of hemisphere, r =

$\tt\frac{2.8}{2} \: cm \\ = 1.4 \: cm$

Length of gulab jamun = 5 cm

Height of cylinder, h = 5 - (1.4+1.4)

= 5 - 2.8

= 2.2 cm

Therefore, Volume of gulab jamun

= Volume of cylinder + 2 × Volume of Hemisphere

$\tt = \pi {r}^{2} h + 2 \times \frac{2}{3} \pi {r}^{3}$

$\tt = \pi {r}^{2} (h + \frac{4}{3} r)$

$\tt = \frac{22}{7} \times 1.4 \times 1.4(2.2 + \frac{4}{3} \times 1.4)$

$\tt= 22 \times 0.2 \times 1.4 \times \frac{6.6 + 5.6}{3}$

$\tt = 6.16 \times \frac{12.2}{3}$

$\tt = \frac{6.16 \times 12.2}{3}$

$\tt= \frac{75.152}{3} \: {cm}^{3}$

Thus, Volume of 45 gulab jamuns

$\tt= 45 \times \frac{75.152}{3}$

$\tt= 1127.28 \: {cm}^{3}$