A spherical shell of outer radius R and inner radius R / 2 contains a solid sphere of radius R / 2 (see figure). The density of the material of the solid sphere is and that of the shell is / 2 . What is the average mass density of the large

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A spherical shell of outer radius R and inner radius R / 2 contains a solid sphere of radius R / 2 (see figure). The density of the material of the solid sphere is and that of the shell is / 2 . What is the average mass density of the larger sphere thus formed?

Quantrex Academy · Accepted Answer

Correct answer: B. 9 / 16

aligned & Average density = Total mass Total volume & = ₁ V₁+ ₂ V₂ V & = 4 3 ( R 2 )^3+ 2 [ 4 3 R ^3- 4 3 ( R 2 )^3 ] 4 3 R ^3 & = 4 3 R ^3 8 + 2 [ 4 3 R ^3- 4 3 R ^3 8 ] 4 3 R ^3 & = 8 + 2 [1- 1 8 ] & = 8 + 2 [ 7 8 ] & = 8 + 7 16 & = 2 +7 16 = 9 16 . aligned

A spherical shell of outer radius R and inner radius R / 2 contains a solid sphere of radius R / 2 (see figure). The density of the material of the solid sphere is and that of the shell is / 2 . What is the average mass density of the larger sphere thus formed?

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