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

Explanation

To find the volume of the block given its length, breadth, and thickness, we will follow these steps:

### Step 1: Identify the given 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 volume (V) of a rectangular block can be calculated using the formula:
\[ V = l \times b \times t \]

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

### Step 3: Perform the multiplication
First, multiply the length and breadth:
\[ 12 \, \text{cm} \times 6 \, \text{cm} = 72 \, \text{cm}^2 \]

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
Next, we need to consider significant figures in our final answer. The number of significant figures in each measurement is as follows:
- Length (12 cm) has **2 significant figures**.
- Breadth (6 cm) has **1 significant figure**.
- Thickness (2.45 cm) has **3 significant figures**.

When multiplying or dividing, the result should have the same number of significant figures as the measurement with the least number of significant figures. Here, the breadth has the least significant figures (1 significant figure).

### Step 5: Round the result
The calculated volume is 176.4 cm³. Since we need to express this in **1 significant figure**, we round it:
- The first significant figure is 1 (in 176.4).
- Since 7 (the next digit) is greater than 5, we round up 1 to 2.

Thus, the volume rounded to 1 significant figure is:
\[ V \approx 200 \, \text{cm}^3 \]

### Final Answer
The volume of the block, expressed according to significant figures, is **200 cm³**.

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