If the diameter of a cylinder is 28 cm and its height is 20 cm then its curved surface area is

Options

A. `880 cm^(2)`
B. `1760 cm^(2)`
C. `3520 cm^(2)`
D. `2640 cm^(2)`

Explanation

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

\[ \text{Curved Surface Area} = 2 \pi r h \]

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

### Step-by-Step Solution:

**Step 1: Find the radius of the cylinder.**
- The diameter of the cylinder is given as 28 cm.
- The radius \( r \) is half of the diameter.

\[ r = \frac{\text{Diameter}}{2} = \frac{28 \, \text{cm}}{2} = 14 \, \text{cm} \]

**Step 2: Identify the height of the cylinder.**
- The height \( h \) is given as 20 cm.

**Step 3: Substitute the values into the formula for the curved surface area.**
- Now we can substitute \( r = 14 \, \text{cm} \) and \( h = 20 \, \text{cm} \) into the formula.

\[ \text{Curved Surface Area} = 2 \pi r h = 2 \times \frac{22}{7} \times 14 \times 20 \]

**Step 4: Calculate the curved surface area.**
- First, calculate \( 2 \times \frac{22}{7} \times 14 \):

\[ 2 \times \frac{22}{7} \times 14 = \frac{2 \times 22 \times 14}{7} = \frac{616}{7} \, \text{cm}^2 \]

- Now multiply this by the height \( h = 20 \):

\[ \text{Curved Surface Area} = \frac{616}{7} \times 20 = \frac{12320}{7} \, \text{cm}^2 \approx 1760 \, \text{cm}^2 \]

### Final Answer:
The curved surface area of the cylinder is approximately \( 1760 \, \text{cm}^2 \).

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