Pressure in a fluid-mechanical properties of fluids

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Question

A piece of copper having an internal cavity weights 264 g in air and 225 g in water. The volume of cavity ( in $c m^{3}$ )is $(d e n s i t y o f c o p p e r = 8.8 g c m^{- 3})$

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Solution

Let $V_{1}$ be the volume of cavity and $V_{2}$ be the volume of copper material ( excluding cavity)
$V_{2} = \frac{264}{8.8} = 30 c {m^{3}}^{}$
Loss of weight =Buoyancy force
$39 g = (v_{1} + v_{2}) ρ_{w} \times g$
$v_{1} + v_{2} = 39 c m^{3}$
$\Rightarrow v_{1} = 9 c m^{3}$

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