The radius of the base of a cone is 14 cm and its height is 48 cm . What is the curved surface area of the cone ?

Answer

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

### Step 1: Identify the given values
- Radius (r) = 14 cm
- Height (h) = 48 cm

### Step 2: Calculate the slant height (l) of the cone
The slant height can be calculated using the Pythagorean theorem:
\[ l = \sqrt{h^2 + r^2} \]
Substituting the values:
\[ l = \sqrt{48^2 + 14^2} \]
Calculating \(48^2\) and \(14^2\):
\[ 48^2 = 2304 \quad \text{and} \quad 14^2 = 196 \]
Adding these:
\[ l = \sqrt{2304 + 196} = \sqrt{2500} \]
Calculating the square root:
\[ l = 50 \text{ cm} \]

### Step 3: Use the formula for the curved surface area (CSA) of the cone
The formula for the curved surface area of a cone is:
\[ \text{CSA} = \pi r l \]
Substituting the values of \(r\) and \(l\):
\[ \text{CSA} = \pi \times 14 \times 50 \]
Calculating the multiplication:
\[ \text{CSA} = 700\pi \text{ cm}^2 \]

### Step 4: Approximate the value of \(\pi\)
Using \(\pi \approx 3.14\):
\[ \text{CSA} \approx 700 \times 3.14 = 2198 \text{ cm}^2 \]

### Final Answer
The curved surface area of the cone is approximately \(2198 \text{ cm}^2\).

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