The length, breadth and thickness of a block are given by l=12 cm , b=6cm and t=2.45 cm. The volume of the block according to the idea of significant figures should be

Options

A. `1xx10^(2)" cm"^(3)`
B. `2xx10^(2)" cm"^(3)`
C. `1.764xx10^(2)" cm"^(3)`
D. None of these

Explanation

To solve the problem of finding the volume of the block with the given dimensions while considering significant figures, we can follow these steps:

### Step 1: Identify the dimensions
The dimensions of the block are:
- Length (l) = 12 cm
- Breadth (b) = 6 cm
- Thickness (t) = 2.45 cm

### Step 2: Calculate the volume
The formula for the volume (V) of a rectangular block is given by:
\[ V = l \times b \times t \]

Substituting the values:
\[ V = 12 \, \text{cm} \times 6 \, \text{cm} \times 2.45 \, \text{cm} \]

### Step 3: Perform the multiplication
Calculating the multiplication step-by-step:
1. First, multiply the length and breadth:
\[ 12 \times 6 = 72 \, \text{cm}^2 \]
2. Now, multiply this result by the thickness:
\[ 72 \, \text{cm}^2 \times 2.45 \, \text{cm} = 176.4 \, \text{cm}^3 \]

### Step 4: Determine significant figures
Now we need to consider the significant figures in the measurements:
- Length (12 cm) has **2 significant figures**.
- Breadth (6 cm) has **1 significant figure**.
- Thickness (2.45 cm) has **3 significant figures**.

The volume will be limited by the measurement with the least number of significant figures, which in this case is the breadth (6 cm) with **1 significant figure**.

### Step 5: Round the volume to the appropriate significant figures
The calculated volume is 176.4 cm³. Since we need to express this with **1 significant figure**, we round it to:
- The first significant figure is '2' (from 176.4), so we round down to 200.

Thus, we express the volume in scientific notation:
\[ V \approx 2 \times 10^2 \, \text{cm}^3 \]

### Final Answer
The volume of the block, considering significant figures, is:
\[ \boxed{2 \times 10^2 \, \text{cm}^3} \]

---