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Question
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.
Solution
Given the inner diameter of the glass = 7cm
So, the radius of the glass
`"r"=7/2 "cm"` = 3.5 cm
Height of the glass, h = 16 cm and
The volume of the cylindrical glass = πr2h
= `22/7xx7/2xx7/2xx16`
= 616 cm3
Now, radius of the hemisphere = Radius of the cylinder
= r = 3.5 cm
Volume of hemisphere = `2/3`πr3
= `2/3xx22/7xx3.5xx3.5xx3.5`
= 89.83cm3
Now,
Apparent capacity of the glass = Volume of cylinder = 616 cm3
The actual capacity of the glass = Total volume of cylinder - Volume of hemisphere
= 616 - 89.83
= 526.17 cm3
Hence,
Apparent capacity of the glass = 616 cm3
and actual capacity of the glass = 526.17 cm3
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Assertion (A)
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Reason (R)
Volume of a cone = πr2h
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