The radius of a sphere is 6.01 cm. Its volume to four significant figures is

Options

A. `909.7 cm^(3)`
B. `909 cm^(3)`
C. `916 cm^(3)`
D. `909.67cm^(3)`

Answer

To find the volume of a sphere with a radius of 6.01 cm to four significant figures, we can follow these steps:

### Step 1: Write down 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 2: Substitute the radius into the formula.
Given that the radius \( r = 6.01 \) cm, we substitute this value into the formula:

\[ V = \frac{4}{3} \pi (6.01)^3 \]

### Step 3: Calculate \( r^3 \).
First, calculate \( (6.01)^3 \):

\[ (6.01)^3 = 6.01 \times 6.01 \times 6.01 = 217.728601 \, \text{cm}^3 \]

### Step 4: Substitute \( r^3 \) back into the volume formula.
Now substitute \( 217.728601 \) into the volume formula:

\[ V = \frac{4}{3} \pi (217.728601) \]

### Step 5: Use the value of \( \pi \).
Using \( \pi \approx 3.14 \):

\[ V = \frac{4}{3} \times 3.14 \times 217.728601 \]

### Step 6: Calculate the volume.
Now calculate the volume:

\[ V \approx \frac{4}{3} \times 3.14 \times 217.728601 \approx 909.297 \, \text{cm}^3 \]

### Step 7: Round the volume to four significant figures.
To round \( 909.297 \) to four significant figures, we look at the fifth digit (which is 9). Since it is greater than 5, we round up:

\[ V \approx 909.3 \, \text{cm}^3 \]

### Step 8: Finalize the answer.
Thus, the volume of the sphere to four significant figures is:

\[ \boxed{909.3 \, \text{cm}^3} \]