The curved surface area of a cylinder with radius 2cm and height 7 cm will be `:`

Options

A. `88 cm^(2)`
B. 88 cm
C. `88 cm^(3)`
D. 44 cm

Answer

To find the curved surface area of a cylinder with a radius of 2 cm and a height of 7 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the formula for the curved surface area of a cylinder:**
The formula for the curved surface area (CSA) of a cylinder is given by:
\[ \text{CSA} = 2\pi rh \]
where \( r \) is the radius and \( h \) is the height of the cylinder.

2. **Substitute the given values into the formula:**
Here, the radius \( r = 2 \) cm and the height \( h = 7 \) cm. Now, substitute these values into the formula:
\[ \text{CSA} = 2 \times \pi \times 2 \times 7 \]

3. **Calculate the value of \( 2 \times 2 \times 7 \):**
First, calculate the product:
\[ 2 \times 2 = 4 \]
\[ 4 \times 7 = 28 \]
So, we have:
\[ \text{CSA} = 28\pi \]

4. **Use the value of \( \pi \):**
For calculations, we can use \( \pi \approx \frac{22}{7} \). Now substitute this value into the equation:
\[ \text{CSA} = 28 \times \frac{22}{7} \]

5. **Simplify the expression:**
First, simplify \( \frac{28}{7} \):
\[ \frac{28}{7} = 4 \]
Now, multiply by 22:
\[ \text{CSA} = 4 \times 22 = 88 \]

6. **State the final answer:**
Therefore, the curved surface area of the cylinder is:
\[ \text{CSA} = 88 \text{ cm}^2 \]