A sphere of material of relative density 8 has a concentric spherical cavity and just sinks in water. If the radius of the sphere is 2 ~cm , then the volume of the cavity is

Step-by-step solution

Let r be the radius of cavity Volume of cavity = 4 3 r ^3 Now, 4 3 (R^3-r^3 ) d m g= 4 3 R^3 d_w g 1- R^3 r^3 = 1 8 R^3 r^3 =1- 1 8 R^3 r^3 = 7 8 r^3= 8 7 R^3= 7 8 (2)^3=7 There Volume of cavity = 4 3 r ^3= 4 3 22 7 7= 88 3