Q. 124.2( 5 Votes )

Find the total volume of a cone having a hemispherical base. If the radius of the base is 21 cm and height 60 cm.

Answer :

Given.


Radius of cone and hemisphere = 21 cm


Total height of cone = 60 cm


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 solid is sum of volume of both cone and hemisphere


Volume of solid = Volume of cone + Volume of Hemisphere


= πr2h + πr3


= πr2[h + 2r]


As height of hemisphere is equal to radius of hemisphere


Then;


Volume of top = × 21 × 21 × [60 + 2 × 21]


= × 21 × 21 × [60 + 42]


= × 21 × 21 × [102]


= 22 × 21 × 102


= 47124 cm3


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