A rectangular block is heated from `0^(@)C` to `100^(@)C`. The percentage increases in its length is 0.10 % what will be the percentage increases in it volume ?

Options

A. `0.03%`
B. `0.10%`
C. `0.30%`
D. none of these

Explanation

To solve the problem of finding the percentage increase in the volume of a rectangular block when it is heated from \(0^\circ C\) to \(100^\circ C\), given that the percentage increase in its length is \(0.10\%\), we can follow these steps:

### Step 1: Understand the relationship between linear and volumetric expansion
The volume \(V\) of a rectangular block can be expressed in terms of its length \(L\):
\[ V = L^3 \]
When the block is heated, its length increases, which in turn affects its volume.

### Step 2: Use the formula for change in volume
The change in volume \(\Delta V\) due to a change in length \(\Delta L\) can be expressed as:
\[ \Delta V = V_0 \cdot 3 \frac{\Delta L}{L} \]
where \(V_0\) is the original volume and \(\frac{\Delta L}{L}\) is the fractional change in length.

### Step 3: Substitute the given values
Given that the percentage increase in length is \(0.10\%\), we can express this as:
\[ \frac{\Delta L}{L} = \frac{0.10}{100} = 0.001 \]
Now substituting this value into the change in volume formula:
\[ \Delta V = 3 \cdot \Delta L = 3 \cdot 0.001 = 0.003 \]

### Step 4: Convert the change in volume to percentage
To find the percentage increase in volume, we can express it as:
\[ \text{Percentage increase in volume} = \Delta V \times 100\% \]
Substituting the value of \(\Delta V\):
\[ \text{Percentage increase in volume} = 0.003 \times 100\% = 0.30\% \]

### Conclusion
Thus, the percentage increase in the volume of the rectangular block when heated from \(0^\circ C\) to \(100^\circ C\) is \(0.30\%\).

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