A hollow metal of mass 180.6 g contains cavity of volume `2.5 cm^(3)` . This metal when placed in water displaces 24 cc of water. Find the specific gravity of metal.

Options

A. 7.6
B. 8.4
C. 10.5
D. 7.2

Answer

To find the specific gravity of the hollow metal, we will follow these steps:

### Step 1: Identify the given values
- Mass of the metal (m) = 180.6 g
- Volume of the cavity (Vc) = 2.5 cm³
- Volume of water displaced = 24 cm³

### Step 2: Calculate the total volume of the metal
The total volume of the metal is equal to the volume of water displaced, which is given as 24 cm³.

### Step 3: Calculate the actual volume of the metal
To find the actual volume of the metal (Vm), we need to subtract the volume of the cavity from the total volume of the metal.
\[ Vm = \text{Total Volume} - \text{Volume of Cavity} \]
\[ Vm = 24 \, \text{cm}^3 - 2.5 \, \text{cm}^3 \]
\[ Vm = 21.5 \, \text{cm}^3 \]

### Step 4: Calculate the density of the metal
Density (ρ) is calculated using the formula:
\[ \rho = \frac{\text{Mass}}{\text{Volume}} \]
Substituting the values:
\[ \rho = \frac{180.6 \, \text{g}}{21.5 \, \text{cm}^3} \]
Calculating this gives:
\[ \rho \approx 8.4 \, \text{g/cm}^3 \]

### Step 5: Calculate the specific gravity of the metal
Specific gravity (SG) is the ratio of the density of the substance to the density of water. Since the density of water is 1 g/cm³, we can calculate:
\[ SG = \frac{\text{Density of Metal}}{\text{Density of Water}} \]
\[ SG = \frac{8.4 \, \text{g/cm}^3}{1 \, \text{g/cm}^3} \]
Thus, the specific gravity of the metal is:
\[ SG = 8.4 \]

### Final Answer
The specific gravity of the metal is **8.4**.

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