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 π=3.14). [3 MARKS]
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 =πr2h
=3.14×2.5×2.5×10 cm3=196.25 cm3
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
23πr3=23×3.14×2.5×2.5×2.5 cm3=32.71 cm3
So, the actual capacity of the glass = apparent capacity of glass - volume of the hemisphere
=(196.25−32.71) cm3
=163.54 cm3