The height of a cone is 7 cm and its radius of base is 3 cm. Find its volume.

Answer

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

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

where:
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone,
- \( \pi \) is a constant approximately equal to \( \frac{22}{7} \) or \( 3.14 \).

### Step-by-Step Solution:

1. **Identify the given values**:
- Radius \( r = 3 \) cm
- Height \( h = 7 \) cm

2. **Substitute the values into the volume formula**:
\[ \text{Volume} = \frac{1}{3} \pi (3)^2 (7) \]

3. **Calculate \( r^2 \)**:
\[ r^2 = 3^2 = 9 \]
So, we can rewrite the volume formula as:
\[ \text{Volume} = \frac{1}{3} \pi (9) (7) \]

4. **Multiply \( 9 \) and \( 7 \)**:
\[ 9 \times 7 = 63 \]
Now the formula becomes:
\[ \text{Volume} = \frac{1}{3} \pi (63) \]

5. **Substitute \( \pi \) with \( \frac{22}{7} \)**:
\[ \text{Volume} = \frac{1}{3} \times \frac{22}{7} \times 63 \]

6. **Simplify the expression**:
- First, calculate \( \frac{63}{7} = 9 \):
\[ \text{Volume} = \frac{1}{3} \times 22 \times 9 \]

7. **Multiply \( 22 \) and \( 9 \)**:
\[ 22 \times 9 = 198 \]
So, we have:
\[ \text{Volume} = \frac{198}{3} \]

8. **Divide \( 198 \) by \( 3 \)**:
\[ \text{Volume} = 66 \text{ cm}^3 \]

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