Q) An empty cone is of radius 3 cm and height 12 cm. Ice-cream is filled in it so that lower part of the cone, which is th of volume of the cone, is unfilled but hemisphere is formed on the top. Find volume of the of ice-cream.

Ans: 

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Volume of the cone = r²h = x (3)² x 12 = 36

When Ice cream is filled in this cone, its  th portion is unfilled and  th gets filled.

Hence, volume of this  th cone = x 36   = 30 ………. (i)

Volume of Icecream’s hemispeherical shape on top of the cone

=        r³     =        x (3)³  = 18  ..……… (ii)

From equations (i) and (ii), we get,

Total Volume of Icecream = 30 + 18 = 48   = 48 x

=          150.72 cm³