Find the curved surface area (in `cm^(2)`) of a right circular cylinder of diameter 7 cm and height 6 cm.

Options

A. 132
B. 110
C. 92
D. 154

Answer

To find the curved surface area of a right circular cylinder, we can use the formula:

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

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

### Step-by-Step Solution:

1. **Identify the Diameter and Calculate the Radius:**
- Given diameter = 7 cm.
- To find the radius, use the formula:
\[ r = \frac{\text{Diameter}}{2} = \frac{7 \text{ cm}}{2} = 3.5 \text{ cm} \]

2. **Identify the Height:**
- Given height \( h = 6 \) cm.

3. **Substitute Values into the Curved Surface Area Formula:**
- Substitute \( r \) and \( h \) into the formula:
\[ \text{CSA} = 2 \pi r h = 2 \times \frac{22}{7} \times 3.5 \times 6 \]

4. **Calculate the Curved Surface Area:**
- First, calculate \( 2 \times \frac{22}{7} \):
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]
- Now, calculate \( \frac{44}{7} \times 3.5 \):
\[ 3.5 = \frac{7}{2} \implies \frac{44}{7} \times \frac{7}{2} = \frac{44}{2} = 22 \]
- Finally, multiply by the height \( h \):
\[ \text{CSA} = 22 \times 6 = 132 \text{ cm}^2 \]

### Final Answer:
The curved surface area of the right circular cylinder is \( 132 \text{ cm}^2 \).

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