A metallic sphere with an internal cavity weighs 40 gwt in air and 20 gwt in water. If the density of the material with cavity be 8 g per ${\mathrm{cm}}^3$ then the volume of cavity is:

Weigth of sphere in air = 40 gwt

Weight of sphere in water = 20 gwt

Loss in weight = (40-20) gf = 20 gwt

Weight of water displaced = loss in weight = 20 gwt

Mass of water displaced = 20 g

Volume of water displaced = 20 ${\mathrm{cm}}^3$

Actual volume of sphere = volume of water displaced

                                       = 20 ${\mathrm{cm}}^3$

Volume of material in the sphere = $\frac{40}{8}= 5 {\mathrm{cm}}^3$

Volume of cavity = (20-5) = 15 ${\mathrm{cm}}^3$