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

Options

A. `220 pi`
B. `180 pi`
C. `250pi`
D. `240 pi`

Answer

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

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

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

### Step 3: Set up the equation
From the problem, we have:
\[ 2\pi r = 20\pi \]

### Step 4: Solve for the radius \(r\)
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 formula for curved surface area
The formula for the curved surface area \(A\) of a cylinder is:
\[ A = 2\pi rh \]
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 formula:
\[ A = 2\pi (10)(12) \]

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

### Step 8: Approximate the value if needed
If we need a numerical approximation, we can use \(\pi \approx 3.14\):
\[ A \approx 240 \times 3.14 \approx 753.6 \text{ cm}^2 \]

### Final Answer
Thus, the curved surface area of the cylinder is \(240\pi \text{ cm}^2\) or approximately \(753.6 \text{ cm}^2\).

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