The dimensions of a wooden block are `1.1m xx 2.36 m x 3.1 m`. The number of significant figures in its volume should be

Options

A. 1
B. 2
C. 3
D. 4

Answer

To find the number of significant figures in the volume of a wooden block with dimensions given as \(1.1 \, \text{m} \times 2.36 \, \text{m} \times 3.1 \, \text{m}\), we can follow these steps:

### Step 1: Identify the dimensions
The dimensions of the wooden block are:
- Length (\(L\)) = \(1.1 \, \text{m}\)
- Width (\(W\)) = \(2.36 \, \text{m}\)
- Height (\(H\)) = \(3.1 \, \text{m}\)

### Step 2: Determine significant figures in each dimension
- \(1.1 \, \text{m}\) has **2 significant figures** (the digits 1 and 1).
- \(2.36 \, \text{m}\) has **3 significant figures** (the digits 2, 3, and 6).
- \(3.1 \, \text{m}\) has **2 significant figures** (the digits 3 and 1).

### Step 3: Calculate the volume
The volume \(V\) of the block can be calculated using the formula:
\[ V = L \times W \times H \]
Substituting the values:
\[ V = 1.1 \, \text{m} \times 2.36 \, \text{m} \times 3.1 \, \text{m} \]

Calculating this step-by-step:
1. First, calculate \(1.1 \times 2.36\):
\[ 1.1 \times 2.36 = 2.596 \]
This result has **2 significant figures** (limited by \(1.1\)).

2. Now, multiply this result by \(3.1\):
\[ 2.596 \times 3.1 = 8.0476 \]
This result has **4 significant figures** (limited by \(2.596\)).

### Step 4: Determine the significant figures in the final volume
When multiplying or dividing, the result should have the same number of significant figures as the measurement with the least significant figures. In this case, the dimensions \(1.1 \, \text{m}\) and \(3.1 \, \text{m}\) both have **2 significant figures**.

Thus, we round \(8.0476\) to **2 significant figures**, which gives us:
\[ V \approx 8.0 \, \text{m}^3 \]

### Step 5: Conclusion
The number of significant figures in the volume of the wooden block is **2**.

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