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. a) `1 xx 10^(2) cm^(3)`
B. b) `2 xx (10^2)cm^3`
C. c) `1.763 xx (10^2)cm^3`
D. d) None of these

Explanation

To solve the problem of calculating the volume of a block given its dimensions and expressing the result in terms of significant figures, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the dimensions of the block:**
- Length (l) = 12 cm
- Breadth (b) = 6 cm
- Thickness (t) = 2.45 cm

2. **Calculate the volume of the block:**
- The formula for the volume (V) of a rectangular block is:
\[ V = l \times b \times t \]
- Substituting the values:
\[ V = 12 \, \text{cm} \times 6 \, \text{cm} \times 2.45 \, \text{cm} \]

3. **Perform the multiplication:**
- First, calculate \(12 \times 6\):
\[ 12 \times 6 = 72 \]
- Next, multiply the result by 2.45:
\[ 72 \times 2.45 = 176.4 \, \text{cm}^3 \]

4. **Determine significant figures:**
- The significant figures in the measurements are:
- Length (12 cm) has 2 significant figures.
- Breadth (6 cm) has 1 significant figure.
- Thickness (2.45 cm) has 3 significant figures.
- The measurement with the least number of significant figures is the breadth (1 significant figure).

5. **Round the volume to the appropriate significant figures:**
- The calculated volume is 176.4 cm³.
- Since the least number of significant figures is 1 (from the breadth), we round 176.4 to 1 significant figure:
- The first significant figure is 1 (from 176.4).
- The next digit is 7, which is greater than 5, so we round up.
- Therefore, 176.4 rounded to 1 significant figure becomes 200.

6. **Express the final answer:**
- The volume can be expressed as:
\[ V = 200 \, \text{cm}^3 \quad \text{or} \quad V = 2 \times 10^2 \, \text{cm}^3 \]

### Final Answer:
The volume of the block, expressed in terms of significant figures, is:
\[ V = 200 \, \text{cm}^3 \quad \text{or} \quad V = 2 \times 10^2 \, \text{cm}^3 \]