The slant height of a cone is 10.5 cm and diametre of base is 14 cm. Find its curved surface area.

Answer

To find the curved surface area of the cone, we can follow these steps:

### Step 1: Identify the given values
- Slant height (l) = 10.5 cm
- Diameter of the base (d) = 14 cm

### Step 2: Calculate the radius (r) of the base
The radius can be calculated using the formula:
\[ r = \frac{d}{2} \]
Substituting the value of the diameter:
\[ r = \frac{14 \text{ cm}}{2} = 7 \text{ cm} \]

### Step 3: Use the formula for the curved surface area (CSA) of a cone
The formula for the curved surface area of a cone is given by:
\[ \text{CSA} = \pi r l \]
Where:
- \( \pi \) is approximately \( \frac{22}{7} \)
- \( r \) is the radius
- \( l \) is the slant height

### Step 4: Substitute the values into the formula
Substituting the values of \( r \) and \( l \):
\[ \text{CSA} = \frac{22}{7} \times 7 \text{ cm} \times 10.5 \text{ cm} \]

### Step 5: Simplify the expression
The \( 7 \) in the numerator and denominator cancels out:
\[ \text{CSA} = 22 \times 10.5 \text{ cm} \]

### Step 6: Calculate \( 22 \times 10.5 \)
To perform the multiplication:
\[ 22 \times 10.5 = 231 \text{ cm}^2 \]

### Step 7: Conclusion
Therefore, the curved surface area of the cone is:
\[ \text{CSA} = 231 \text{ cm}^2 \]

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