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A juice seller was serving his customers using glasses as shown in fiqure. The inner diameter of the cylindrical qlass was $5 cm$ but bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was $10 cm$ , then what is the apparent and actual capacity of the glass? (Use $π = 3.14)$

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163 cm 3

160.44 cm 3

163.54 cm 3

162 cm 3

answer is C.

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Detailed Solution

Given that the inner diameter of the cylindrical glass is

5 cm

and the height is 10cm.
Question Image

We have the following formula,
Volume of a cylinder

= π r 2 h

Volume of a hemisphere

= 23 π r 3

The radius will be,

r = D 2 = 52 cm

Apparent capacity is the volume of the cylinder,

= 3.14 × 52 × 52 × 10 = 196.25 cm 3

Volume of the hemisphere will be,

= 23 × 3.14 × 52 × 52 × 52 = 32.71 c m 3

Actual capacity = apparent capacity - Volume of hemisphere

= 196.25 − 32.71 = 163.54 cm 3

Thus, the actual capacity is

163.54 cm 3

.
Therefore the correct option is 3.

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