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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 π=3.14). [3 MARKS]

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Solution

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

=(196.2532.71) cm3

=163.54 cm3


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