The height of a cone is 24 cm and radius of base is 7 cm. Find its salant height.

Answer

To find the slant height of a cone given its height and radius, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Height (h) of the cone = 24 cm
- Radius (r) of the base = 7 cm

2. **Recall the Formula for Slant Height**:
The slant height (L) of a cone can be calculated using the Pythagorean theorem:
\[ L^2 = h^2 + r^2 \]

3. **Substitute the Given Values into the Formula**:
\[ L^2 = (24 \, \text{cm})^2 + (7 \, \text{cm})^2 \]

4. **Calculate the Squares**:
- Calculate \(24^2\):
\[ 24^2 = 576 \]
- Calculate \(7^2\):
\[ 7^2 = 49 \]

5. **Add the Squares**:
\[ L^2 = 576 + 49 = 625 \]

6. **Take the Square Root to Find the Slant Height**:
\[ L = \sqrt{625} \]
\[ L = 25 \, \text{cm} \]

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