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.
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=9.5−3.5=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