Q. 63.5( 12 Votes )

A playing top is made up of steel. The top is shaped like a cone surmounted by a hemisphere. The total height of top is 5 cm and the diameter of the top is 3.5 cm. Find the volume of the top.

Answer :

Given.


Diameter of cone and hemisphere = 3.5cm


Total height of top = 5cm


Formula used/Theory.


Volume of Cone = πr2h


Volume of hemisphere = πr3


As we put Cone on hemisphere


The circle part of both cone and hemisphere will attach


Volume of top is sum of volume of both cone and hemisphere


Volume of top = Volume of cone + Volume of Hemisphere


= πr2h + πr3


= πr2[h + 2r]


Radius of hemisphere =


= = 1.75


As height of hemisphere is equal to radius of hemisphere


Then;


Height of cone = Height of top – Radius


= 5cm – 1.75cm


= 3.25 cm


Volume of top = × 1.75 × 1.75 × [3.25 + 2 × 1.75]


= × 1.75 × 1.75 × [3.25 + 3.5]


= × 1.75 × 1.75 × [6.75]


= 22 × 0.25 × 1.75 × 2.25


= 21.65 cm3


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