Find the curved surface area (in `cm^(2)`) of a right circular cylinder of diameter 21 cm and height 10 cm.

Options

A. 594
B. 530
C. 472
D. 660

Answer

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

\[ \text{Curved Surface Area (C.S.A)} = 2 \pi r h \]

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:

1. **Determine the radius**:
- The diameter of the cylinder is given as 21 cm.
- The radius \( r \) is half of the diameter:
\[ r = \frac{\text{diameter}}{2} = \frac{21 \, \text{cm}}{2} = 10.5 \, \text{cm} \]

2. **Identify the height**:
- The height \( h \) of the cylinder is given as 10 cm.

3. **Substitute the values into the formula**:
- Now, substitute \( r = 10.5 \, \text{cm} \) and \( h = 10 \, \text{cm} \) into the formula for the curved surface area:
\[ \text{C.S.A} = 2 \pi r h = 2 \times \frac{22}{7} \times 10.5 \times 10 \]

4. **Calculate the C.S.A**:
- First, calculate \( 2 \times \frac{22}{7} \):
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]
- Next, calculate \( \frac{44}{7} \times 10.5 \):
\[ 10.5 = \frac{21}{2} \implies \frac{44}{7} \times \frac{21}{2} = \frac{44 \times 21}{14} = \frac{924}{14} = 66 \]
- Finally, multiply by the height \( h \):
\[ \text{C.S.A} = 66 \times 10 = 660 \, \text{cm}^2 \]

5. **Conclusion**:
- The curved surface area of the cylinder is \( 660 \, \text{cm}^2 \).