What is the curved surface area (in `cm^2`) of a cylinder having radius of base as 21 cm and height as 30 cm?

Options

A. 3740
B. 3850
C. 1980
D. 3960

Answer

To find the curved surface area (CSA) of a cylinder, we can use the formula:

\[ \text{Curved Surface Area (CSA)} = 2\pi rh \]

where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is a constant approximately equal to \( 3.14 \) or can be taken as \( \frac{22}{7} \) for calculations.

### Step-by-step solution:

1. **Identify the values**:
- Radius \( r = 21 \) cm
- Height \( h = 30 \) cm

2. **Substitute the values into the formula**:
\[ \text{CSA} = 2 \times \pi \times r \times h \]
Using \( \pi \approx \frac{22}{7} \):
\[ \text{CSA} = 2 \times \frac{22}{7} \times 21 \times 30 \]

3. **Calculate \( 2 \times \frac{22}{7} \)**:
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]

4. **Multiply by the radius**:
\[ \frac{44}{7} \times 21 = \frac{44 \times 21}{7} \]
Since \( 21 = \frac{147}{7} \):
\[ \frac{44 \times 21}{7} = \frac{44 \times 147}{49} = 44 \times 3 = 132 \]

5. **Now multiply by the height**:
\[ \text{CSA} = 132 \times 30 = 3960 \text{ cm}^2 \]

Thus, the curved surface area of the cylinder is \( 3960 \text{ cm}^2 \).

### Final Answer:
The curved surface area of the cylinder is \( 3960 \text{ cm}^2 \).