The diameter of a sphere is `3.34 m`. Calculate its volume with due regard to significant figures.

Explanation

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

### Step 1: Identify the formula for the volume of a sphere
The volume \( V \) of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.

### Step 2: Calculate the radius from the diameter
The diameter \( d \) of the sphere is given as \( 3.34 \, m \). The radius \( r \) can be calculated using the formula:
\[ r = \frac{d}{2} \]
Substituting the value of the diameter:
\[ r = \frac{3.34 \, m}{2} = 1.67 \, m \]

### Step 3: Substitute the radius into the volume formula
Now, we can substitute the value of the radius into the volume formula:
\[ V = \frac{4}{3} \pi (1.67 \, m)^3 \]

### Step 4: Calculate \( (1.67)^3 \)
Calculating \( (1.67)^3 \):
\[ (1.67)^3 = 4.641 \, m^3 \]

### Step 5: Calculate the volume
Now substitute \( (1.67)^3 \) back into the volume formula:
\[ V = \frac{4}{3} \pi (4.641 \, m^3) \]
Using \( \pi \approx 3.14 \):
\[ V = \frac{4}{3} \times 3.14 \times 4.641 \]
Calculating this gives:
\[ V \approx \frac{4 \times 3.14 \times 4.641}{3} \approx \frac{58.191}{3} \approx 19.397 \, m^3 \]

### Step 6: Apply significant figures
The diameter \( 3.34 \, m \) has three significant figures. Therefore, the volume should also be expressed with three significant figures:
\[ V \approx 19.4 \, m^3 \]

### Final Answer
The volume of the sphere is approximately:
\[ \boxed{19.4 \, m^3} \]

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