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Question

A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find the volume of the solid.

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Solution


Total height of the solid =9.5 cm
Radius of the cone = Radius of the hemisphere =r=3.5 cm

Radius of the hemisphere = height of hemisphere =3.5 cm

Height of cone,( h) = total height of the solid - height of the hemisphere

h=9.53.5=6 cm

The volume of the solid = volume of cone + volume of the hemisphere

=13πr2h+23πr3
=13πr2(h+2r)
=13×227×3.5×3.5×(6+2×3.5)
=13×227×3.5×3.5×(6+7)
=13×227×3.5×3.5×(13)
=13×22×.5×3.5×(13)
=500.53
=166.83 cm3

Hence, the volume of the solid is 166.83 cm3



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