The diameter of the base of a cone is 6 cm and height is 4 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
- Diameter of the base of the cone = 6 cm
- Height of the cone (h) = 4 cm

### Step 2: Calculate the radius of the base of the cone
The radius (r) is half of the diameter.
\[ r = \frac{\text{Diameter}}{2} = \frac{6 \text{ cm}}{2} = 3 \text{ cm} \]

### Step 3: Use the Pythagorean theorem to find the slant height (l)
The slant height (l) can be found using the Pythagorean theorem, which states:
\[ l^2 = h^2 + r^2 \]
Substituting the values:
\[ l^2 = (4 \text{ cm})^2 + (3 \text{ cm})^2 = 16 + 9 = 25 \]
Taking the square root:
\[ l = \sqrt{25} = 5 \text{ cm} \]

### Step 4: Calculate the curved surface area (CSA) of the cone
The formula for the curved surface area of a cone is:
\[ \text{CSA} = \pi r l \]
Using \(\pi \approx \frac{22}{7}\):
\[ \text{CSA} = \frac{22}{7} \times 3 \text{ cm} \times 5 \text{ cm} \]
Calculating this:
\[ \text{CSA} = \frac{22 \times 15}{7} = \frac{330}{7} \text{ cm}^2 \]
Calculating the division:
\[ \text{CSA} \approx 47.14 \text{ cm}^2 \]

### Final Result
The curved surface area of the cone is approximately \( \frac{330}{7} \text{ cm}^2 \) or \( 47.14 \text{ cm}^2 \).

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