A piece of Copper having an internal cavity weighs 264 g in air and 221 g in water. Density of Copper is 8.8 g/cc and that of water is 1 g/cc. Which of the following is the volume of cavity?

(A) 30 cc
(B) 43 cc
(C) 73 cc
(D) 13 cc

Solution

Apparent weight in water $W’=W-F_B$ where W = Normal weight and $F_B$ is the buoyant force.

So, $F_B$ = Weight of water displaced = $V_{Body} \times  \rho_{Water} \times g = W – W’$

$\therefore V_{Body} .1 . g = 264 g – 221 g $

$\therefore V_{Body} = 43 cc $

Now, $V_{Cavity} = V_{Body} – V_{Shaded\, Region=Copper}$

$\therefore V_{Cavity} = 43 cc – \frac {m_{Copper}}{\rho_{Copper}}$

$\therefore V_{Cavity} = 43 cc – \frac {264}{8.8}$

$\therefore V_{Cavity} = 13 cc$

Hence, (D)