The height of a right circular cone is 7 cm and radius is 24 cm. Find the slant height of the cone.

Answer

To find the slant height of a right circular cone, we can use the Pythagorean theorem. The formula for the slant height (L) of a cone is given by:

\[ L = \sqrt{H^2 + R^2} \]

where:
- \( H \) is the height of the cone,
- \( R \) is the radius of the base of the cone.

### Step-by-Step Solution:

1. **Identify the given values**:
- Height (H) = 7 cm
- Radius (R) = 24 cm

2. **Write the formula for slant height**:
\[ L = \sqrt{H^2 + R^2} \]

3. **Substitute the given values into the formula**:
\[ L = \sqrt{7^2 + 24^2} \]

4. **Calculate \( H^2 \) and \( R^2 \)**:
- \( H^2 = 7^2 = 49 \)
- \( R^2 = 24^2 = 576 \)

5. **Add \( H^2 \) and \( R^2 \)**:
\[ L = \sqrt{49 + 576} \]
\[ L = \sqrt{625} \]

6. **Calculate the square root**:
\[ L = 25 \]

7. **Conclusion**:
The slant height of the cone is \( 25 \) cm.

### Final Answer:
The slant height of the cone is 25 cm.