Q21 of 51 Page 13

A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and diameter of the base is 4 cm. If a right circular cylinder circumscribes the toy, find how much more space it will cover?

Given: Radius of cone = radius of cylinder = radius of hemisphere = = 2 cm


Height of cone = 2 cm


To find: Volume of cylinder after toy is inserted.



Formula used:


Volume of cylinder = πr2h


Volume of cone =


Volume of hemisphere =


Explanation:


Volume of cone =




Volume of hemisphere =




Volume of toy = Volume of cone + Volume of hemisphere





= 8π


Now the height of cylinder = height of cone + height of hemisphere


As height of hemisphere = radius of hemisphere


⇒ Height of hemisphere = 2 cm


⇒ height of cylinder = 2 cm + 2 cm = 4 cm


Volume of cylinder = πr2h


= π(2)2(4)


= 16π cm3


Volume of cylinder after toy is inserted = Volume of cylinder – volume of toy


= 16π – 8π


= 8π cm3


Hence the remaining volume is 8π cm3.


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