The curved surface area of a right circular cone of radius 14 cm is 440 sq cm. What is the slant height of the cone?

Options

A. 10 cm
B. 11 cm
C. 12 cm
D. 13 cm

Answer

To find the slant height of the cone, we can use the formula for the curved surface area of a right circular cone:

\[ \text{Curved Surface Area} = \pi r l \]

Where:
- \( r \) is the radius of the cone
- \( l \) is the slant height of the cone
- \( \pi \) is approximately \( \frac{22}{7} \)

### Step-by-Step Solution:

1. **Identify the given values:**
- Curved Surface Area (CSA) = 440 cm²
- Radius (r) = 14 cm

2. **Substitute the known values into the formula:**
\[ 440 = \pi \times 14 \times l \]
Using \( \pi \approx \frac{22}{7} \):
\[ 440 = \frac{22}{7} \times 14 \times l \]

3. **Simplify the equation:**
- First, calculate \( \frac{22}{7} \times 14 \):
\[ \frac{22 \times 14}{7} = \frac{308}{7} = 44 \]
Therefore, the equation becomes:
\[ 440 = 44 \times l \]

4. **Solve for \( l \):**
- Divide both sides by 44:
\[ l = \frac{440}{44} = 10 \text{ cm} \]

5. **Conclusion:**
The slant height of the cone is \( 10 \) cm.