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 of length 5 cm and diameter 2.8 cm.

(a) 383 cm³ 

(b) 833 cm³ 

(c) 338 cm³ 

(d) 388 cm³

Answer 1

Answer: (c) =338 cm³

The gulab jamun can be considered as the combination of three solids as shown in the given diagram. 

Here, radius of the hemispherical ends = radius of the cylinder (r) = 1.4 cm

Height of the cylindrical part (h) = 5 – (1.4 + 1.4) cm 

= 2.2 cm. 

∴  Volume of one gulab jamun = 2 × (Volume of hemisphere) + Volume of cylinder 

=  \(2\times \big[\frac{2}{3}\pi r^3\big]\) + \(\pi r^2 h\) = \(\pi r^2 \big(\frac{4}{3}r+h\big)\) 

= \(\frac{22}{7}\times 1.4 \times 1.4 \big[\frac{4}{3}\times1.4+2.2\big]\)

= \(\frac{22}{7}\times \frac{14}{10} \times \frac{14}{10} \big[\frac{4}{3}\times\frac{14}{10}+\frac{22}{10}\big]\) 

= \(\frac{154}{25}\times \frac{61}{15} = \frac{9394}{375} \,cm^3\)

∴ Quantity of syrup found in 45 gulab jamuns 

= 30% of\(\big(45\times \frac{9394}{375}\big)\) 

= \(\frac{3}{10} \times\) \(\big(45\times \frac{9394}{375}\big)\) = 338.184

≈ 338cm³