The slant height of the cone is 17 cm and its radius is 8 cm. Find its height.

Options

A. 21 cm
B. 15 cm
C. 12 cm
D. 14 cm

Answer

To find the height of the cone given its slant height and radius, we can use the Pythagorean theorem. Here are the steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Slant height (L) = 17 cm
- Radius (r) = 8 cm
- Height (h) = ?

2. **Use the Pythagorean theorem**:
The relationship between the slant height (L), radius (r), and height (h) of the cone can be expressed as:
\[ L^2 = h^2 + r^2 \]

3. **Substitute the known values into the equation**:
\[ 17^2 = h^2 + 8^2 \]

4. **Calculate the squares**:
- \(17^2 = 289\)
- \(8^2 = 64\)

Now, substitute these values into the equation:
\[ 289 = h^2 + 64 \]

5. **Rearrange the equation to solve for \(h^2\)**:
\[ h^2 = 289 - 64 \]
\[ h^2 = 225 \]

6. **Take the square root to find \(h\)**:
\[ h = \sqrt{225} = 15 \text{ cm} \]

7. **Conclusion**:
The height of the cone is **15 cm**.