An ornament weighs 36 g in air and 34 g in water. The goldsmith...

Weight of the ornament in air $= 36 \text{ g}$

Weight of the ornament in water $= 34 \text{ g}$

Loss of weight in water $= 36 - 34 = 2 \text{ g}$

The loss of weight is equal to the weight of the water displaced. Since the density of water is $1 \text{ g/cm}^3$, the total volume of the ornament is:

$V = 2 \text{ cm}^3$

The mass of gold in the ornament is $36 \text{ g}$ and its specific gravity is $19.3$. The volume of actual gold is:

$V_{\text{gold}} = \dfrac{36}{19.3} \approx 1.865 \text{ cm}^3$

The volume of the cavities is the difference between the total volume and the volume of gold:

$V_{\text{cavity}} = V - V_{\text{gold}} = 2 - 1.865 = 0.135 \text{ cm}^3$