The density of aluminium is `2.7 g cm^(-3)` and of brass is `84 g cm^(-3)` . For the same mass, the volume of :

Options

A. both will be same
B. aluminium will be less than that of brass
C. aluminium will be more than that of brass
D. nothing can be said.

Answer

To solve the problem, we need to find the volume of both aluminum and brass for the same mass and compare them. We know the formula for density, which is:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

From this, we can derive the formula for volume:

\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]

### Step-by-Step Solution:

1. **Identify the given values:**
- Density of aluminum (\(D_{Al}\)) = \(2.7 \, \text{g/cm}^3\)
- Density of brass (\(D_{Br}\)) = \(84 \, \text{g/cm}^3\)
- Assume a mass (\(M\)) = \(10 \, \text{g}\) for both materials.

2. **Calculate the volume of aluminum:**
\[ V_{Al} = \frac{M}{D_{Al}} = \frac{10 \, \text{g}}{2.7 \, \text{g/cm}^3} \approx 3.70 \, \text{cm}^3 \]

3. **Calculate the volume of brass:**
\[ V_{Br} = \frac{M}{D_{Br}} = \frac{10 \, \text{g}}{84 \, \text{g/cm}^3} \approx 0.119 \, \text{cm}^3 \]

4. **Compare the volumes:**
- Volume of aluminum (\(V_{Al}\)) ≈ \(3.70 \, \text{cm}^3\)
- Volume of brass (\(V_{Br}\)) ≈ \(0.119 \, \text{cm}^3\)

5. **Conclusion:**
Since \(3.70 \, \text{cm}^3\) (volume of aluminum) is much greater than \(0.119 \, \text{cm}^3\) (volume of brass), we can conclude that the volume of aluminum is more than that of brass.

### Final Answer:
The volume of aluminum is more than that of brass.