A

Step 1: Calculate the mass of ice melted using the volume change.
Volume of water displaced = 0.15 cm\textsuperscript{3}.
Since the specific gravity of ice = 0.92, the density of ice = 0.92 g/cm\textsuperscript{3}.
Mass of ice melted = Volume \times Density = 0.15 \text{ cm}\textsuperscript{3} \times 0.92 \text{ g/cm}\textsuperscript{3} = 0.138 g.

Step 2: Calculate the heat absorbed by the melted ice.
Heat absorbed (Q) = mass of ice melted \times latent heat of fusion = 0.138 g \times 80 \text{ cal/g} = 11.04 \text{ cal}.

Step 3: Set up the heat transfer equation.
The heat lost by the metal piece = Heat gained by the ice.
Let c be the specific heat of the metal: \( Q_{lost} = m \cdot c \cdot \Delta T \).
The mass of the metal = 15 g and the change in temperature (\Delta T) = 100ºC - 0ºC = 100ºC.
Therefore, we have: \( 15 \cdot c \cdot 100 = 11.04 \).

Step 4: Solve for c.
\( c = \frac{11.04}{15 \cdot 100} = \frac{11.04}{1500} = 0.00736 \text{ cal/g}ºC.

Thus, the specific heat of the metal is approximately 0.00736 cal/gºC.