The inner diameter of a glass is 7 cm and it has a raised portion in the bottom in the shape of a hemisphere, as shown in the figure. If the height of the glass is 16 cm, find the apparent capacity and the actual capacity of the glass.
Inner diameter of a glass = 7 cm
Inner radius of glass = r = 7/2 cm = 3.5 cm
Height of glass = h = 16 cm
Apparent capacity of glass = πr2h
= 22/7 × 3.5 × 3.5 × 16 cm3
= 616 cm3
Volume of the hemisphere in the bottom = 2/3 πr3
= 2/3 × 22/7 × 3.53 cm3
= 89.83 cm3
Actual capacity of the class = Apparent capacity of glass – Volume of the hemisphere
Actual capacity of the class = 616 cm3 – 89.83 cm3 = 526.17 cm3
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