Question

A juice seller was serving his customers using glasses as shown in Fig. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the apparent capacity of the glass and its actual capacity. (Use $\pi =3.14$). [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

Since the inner diameter of the glass = 5 cm and height = 10 cm,

The apparent capacity of the glass $=\pi r^{2}h$

$=3.14\times 2.5\times 2.5\times 10c{m}^3=196.25c{m}^3$

But the actual capacity of the glass is less by the volume of the hemisphere at the base of the glass.

i.e., it is less by
$\frac{2}{3}\pi r^3=\frac{2}{3}\times 3.14\times 2.5\times 2.5\times 2.5c{m}^3=32.71c{m}^3$

So, the actual capacity of the glass = apparent capacity of glass - volume of the hemisphere

$=(196.25-32.71)c{m}^3$

$=163.54c{m}^3$