A piece of copper having an internal cavity weights 264 g in air and 221 g in water. Find the volume of the cavity. Density of copper is `8.8 g//cm^(3)`

Answer

To find the volume of the cavity in the copper piece, we can follow these steps:

### Step 1: Calculate the weight of the water displaced
The weight of the copper piece in air is given as 264 g, and its weight in water is 221 g. The difference in weight when submerged in water is due to the buoyant force acting on it.

\[ \text{Buoyant Force} = \text{Weight in air} - \text{Weight in water} = 264 \, \text{g} - 221 \, \text{g} = 43 \, \text{g} \]

### Step 2: Convert the buoyant force to volume of water displaced
The buoyant force is equal to the weight of the water displaced by the volume of the object submerged. Since the density of water is approximately \(1 \, \text{g/cm}^3\), the volume of water displaced can be calculated as:

\[ \text{Volume of water displaced} = \frac{\text{Buoyant Force}}{\text{Density of water}} = \frac{43 \, \text{g}}{1 \, \text{g/cm}^3} = 43 \, \text{cm}^3 \]

### Step 3: Calculate the volume of the copper piece
Next, we need to find the volume of the entire copper piece. The density of copper is given as \(8.8 \, \text{g/cm}^3\). The volume of the copper piece can be calculated using its weight in air:

\[ \text{Volume of copper piece} = \frac{\text{Weight in air}}{\text{Density of copper}} = \frac{264 \, \text{g}}{8.8 \, \text{g/cm}^3} = 30 \, \text{cm}^3 \]

### Step 4: Calculate the volume of the cavity
The volume of the cavity can be found by subtracting the volume of the copper piece from the volume of water displaced:

\[ \text{Volume of cavity} = \text{Volume of water displaced} - \text{Volume of copper piece} = 43 \, \text{cm}^3 - 30 \, \text{cm}^3 = 13 \, \text{cm}^3 \]

### Final Answer
The volume of the cavity in the copper piece is \(13 \, \text{cm}^3\).

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