The radius of a sphere is `1.41`. its volume to an appropring number of significant figure is

Options

A. `11.73cm^(3)`
B. `11.736cm^(3)`
C. `11.7cm^(3)`
D. `117cm^(3)`

Explanation

To solve the problem of finding the volume of a sphere with a radius of 1.41 cm to the appropriate number of significant figures, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data**:
- The radius \( r \) of the sphere is given as \( 1.41 \) cm.

2. **Recall the Formula for the Volume of a Sphere**:
- The formula for the volume \( V \) of a sphere is:
\[ V = \frac{4}{3} \pi r^3 \]

3. **Substitute the Value of the Radius into the Formula**:
- Substitute \( r = 1.41 \) cm into the volume formula:
\[ V = \frac{4}{3} \pi (1.41)^3 \]

4. **Calculate \( r^3 \)**:
- First, calculate \( (1.41)^3 \):
\[ (1.41)^3 = 2.8021 \]

5. **Calculate the Volume**:
- Now substitute \( (1.41)^3 \) back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 2.8021 \]
- Calculate \( V \):
\[ V \approx \frac{4}{3} \times 3.14 \times 2.8021 \approx 11.764 \]

6. **Round to the Appropriate Number of Significant Figures**:
- The radius \( 1.41 \) has three significant figures. Therefore, we need to round \( 11.764 \) to three significant figures:
- The first three significant digits are \( 1, 1, \) and \( 7 \). The next digit is \( 6 \), which is greater than \( 5 \), so we round up:
\[ 11.764 \rightarrow 11.8 \]

7. **Final Answer**:
- Thus, the volume of the sphere, rounded to three significant figures, is:
\[ V \approx 11.8 \, \text{cm}^3 \]

### Summary:
The volume of the sphere with a radius of \( 1.41 \) cm, rounded to the appropriate number of significant figures, is \( 11.8 \, \text{cm}^3 \).