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 a cone, we can follow these steps:

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

### Step 2: Calculate the radius of the base
The radius (r) is half of the diameter.
\[ r = \frac{\text{Diameter}}{2} = \frac{14 \text{ cm}}{2} = 7 \text{ cm} \]

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

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

### Step 5: Simplify the expression
First, notice that the \( 7 \) in the numerator and denominator cancels out:
\[ \text{CSA} = 22 \times 10.5 \text{ cm}^2 \]

### Step 6: Calculate the final value
Now, we calculate \( 22 \times 10.5 \):
\[ 22 \times 10.5 = 231 \text{ cm}^2 \]

### Final Answer
The curved surface area of the cone is \( 231 \text{ cm}^2 \).

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