The radius of the base of a cone is 7 cm and the height is 6cm. Its volume is `( pi = ( 22)/( 7))` `:`

Options

A. 924 `cm^(3)`
B. `308 cm^(3)`
C. `1232 cm^(3)`
D. None of these

Answer

To find the volume of the cone, we will use the formula for the volume of a cone:

\[ V = \frac{1}{3} \pi r^2 h \]

where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cone,
- \( \pi \) is a constant (given as \( \frac{22}{7} \)).

### Step-by-Step Solution

1. **Identify the given values:**
- Radius \( r = 7 \) cm
- Height \( h = 6 \) cm
- \( \pi = \frac{22}{7} \)

2. **Substitute the values into the volume formula:**
\[ V = \frac{1}{3} \times \pi \times r^2 \times h \]
\[ V = \frac{1}{3} \times \frac{22}{7} \times (7)^2 \times (6) \]

3. **Calculate \( r^2 \):**
\[ r^2 = 7^2 = 49 \]

4. **Substitute \( r^2 \) back into the volume formula:**
\[ V = \frac{1}{3} \times \frac{22}{7} \times 49 \times 6 \]

5. **Calculate \( \frac{1}{3} \times 6 \):**
\[ \frac{1}{3} \times 6 = 2 \]

6. **Now substitute this back into the formula:**
\[ V = 2 \times \frac{22}{7} \times 49 \]

7. **Calculate \( 2 \times 49 \):**
\[ 2 \times 49 = 98 \]

8. **Now substitute this back into the formula:**
\[ V = \frac{98 \times 22}{7} \]

9. **Divide \( 98 \) by \( 7 \):**
\[ \frac{98}{7} = 14 \]

10. **Now multiply by \( 22 \):**
\[ V = 14 \times 22 = 308 \]

11. **Final result:**
\[ V = 308 \text{ cm}^3 \]

### Conclusion
The volume of the cone is \( 308 \text{ cm}^3 \).