The volume of a cone having radius 3 cm and height 7 cm will be :

Options

A. `166 cm^3`
B. `66 cm^3`
C. `266 cm^3`
D. None of these

Answer

To find the volume of a cone with a radius of 3 cm and a height of 7 cm, we will use the formula for the volume of a cone:

### Step-by-Step Solution:

1. **Write down 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, and \( h \) is the height.

2. **Substitute the values of radius and height into the formula:**
- Given \( r = 3 \) cm and \( h = 7 \) cm.
\[ V = \frac{1}{3} \pi (3)^2 (7) \]

3. **Calculate \( r^2 \):**
\[ r^2 = 3^2 = 9 \]
So, the equation becomes:
\[ V = \frac{1}{3} \pi (9) (7) \]

4. **Multiply \( 9 \) and \( 7 \):**
\[ 9 \times 7 = 63 \]
Now, substitute this back into the equation:
\[ V = \frac{1}{3} \pi (63) \]

5. **Use the value of \( \pi \):**
- We can use \( \pi \approx \frac{22}{7} \).
\[ V = \frac{1}{3} \times \frac{22}{7} \times 63 \]

6. **Simplify the expression:**
- First, simplify \( \frac{63}{7} \):
\[ \frac{63}{7} = 9 \]
- Now, substitute this back into the equation:
\[ V = \frac{1}{3} \times 22 \times 9 \]

7. **Calculate \( 22 \times 9 \):**
\[ 22 \times 9 = 198 \]
So, we have:
\[ V = \frac{198}{3} \]

8. **Divide \( 198 \) by \( 3 \):**
\[ \frac{198}{3} = 66 \]
Therefore, the volume of the cone is:
\[ V = 66 \text{ cm}^3 \]

### Final Answer:
The volume of the cone is \( 66 \text{ cm}^3 \).