The perimeter of base of cylinder is 20π cm. If the height of cylinder is 12 cm, then what will be its curved surface area (in `cm^(2)`) ?

Options

A. 220n
B. 180n
C. 250n
D. 240n

Answer

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

### Step 1: Understand the given information
We know that the perimeter (circumference) of the base of the cylinder is given as \(20\pi\) cm, and the height of the cylinder is \(12\) cm.

### Step 2: Relate the perimeter to the radius
The formula for the perimeter (circumference) of the base of a cylinder is given by:
\[ C = 2\pi r \]
where \(r\) is the radius of the base.

### Step 3: Set up the equation
Since the perimeter is \(20\pi\) cm, we can set up the equation:
\[ 2\pi r = 20\pi \]

### Step 4: Solve for the radius
To find \(r\), we can divide both sides of the equation by \(2\pi\):
\[ r = \frac{20\pi}{2\pi} = 10 \text{ cm} \]

### Step 5: Use the radius to find the curved surface area
The formula for the curved surface area (CSA) of a cylinder is given by:
\[ \text{CSA} = 2\pi rh \]
where \(h\) is the height of the cylinder.

### Step 6: Substitute the values into the formula
Now, substituting \(r = 10\) cm and \(h = 12\) cm into the CSA formula:
\[ \text{CSA} = 2\pi \times 10 \times 12 \]

### Step 7: Calculate the CSA
Calculating this gives:
\[ \text{CSA} = 2\pi \times 10 \times 12 = 240\pi \text{ cm}^2 \]

### Final Answer
Thus, the curved surface area of the cylinder is \(240\pi \text{ cm}^2\).

---