The diameter of a sphere is 1.23 m. Find its volume with due regard to the significant figures.

Explanation

To find the volume of a sphere given its diameter, we can follow these steps:

### Step 1: Calculate the radius of the sphere
The diameter of the sphere is given as 1.23 m. The radius (r) is half of the diameter.

\[ r = \frac{\text{diameter}}{2} = \frac{1.23 \, \text{m}}{2} = 0.615 \, \text{m} \]

### Step 2: Use the formula for the volume of a sphere
The formula for the volume (V) of a sphere is given by:

\[ V = \frac{4}{3} \pi r^3 \]

### Step 3: Substitute the radius into the volume formula
Now, we substitute the radius we calculated into the volume formula. We will use \(\pi \approx 3.14\).

\[ V = \frac{4}{3} \times 3.14 \times (0.615)^3 \]

### Step 4: Calculate \(r^3\)
First, we need to calculate \(0.615^3\):

\[ 0.615^3 = 0.615 \times 0.615 \times 0.615 \approx 0.233 \]

### Step 5: Calculate the volume
Now we can calculate the volume:

\[ V = \frac{4}{3} \times 3.14 \times 0.233 \]

Calculating this gives:

\[ V \approx \frac{4 \times 3.14 \times 0.233}{3} \approx \frac{2.93476}{3} \approx 0.97825333 \]

### Step 6: Round to the correct number of significant figures
The original diameter (1.23 m) has three significant figures, so we need to round our volume to three significant figures as well.

\[ V \approx 0.97825333 \, \text{m}^3 \rightarrow 0.978 \, \text{m}^3 \]

### Step 7: Final rounding
Since the last digit (8) is followed by a 2, we do not round up, so the final volume is:

\[ V \approx 0.978 \, \text{m}^3 \]

### Final Answer:
The volume of the sphere is approximately **0.978 m³**.

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