JAMB 1985 · UME · Q39

Solid mensuration

A solid sphere of radius 4 cm has a mass of 64 kg. What will be the mass of a shell of the same metal whose internal and external radii are 2 cm and 3 cm respectively?

Worked solution (try it first)

Same metal, so mass is proportional to volume, and the volume of a sphere is proportional to $r^3$ .
The shell's volume is the outer sphere minus the inner one, which goes with $3^3 - 2^3 = 27 - 8 = 19$ .
The solid sphere goes with $4^3 = 64$ .
So the shell's mass is $64 \times \frac{19}{64} = 19$ kg, option C.

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