The diameter of the base of a right circular cylinder is 28 cm and its height is 21cm . Its curved surface area is `:`

Options

A. 588` cm^(2)`
B. 1848` cm^(2)`
C. 924 `cm^(2)`
D. 1386 `cm^(2)`

Answer

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

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Diameter of the base of the cylinder = 28 cm
- Height of the cylinder (h) = 21 cm

2. **Calculate the Radius:**
- The radius (r) is half of the diameter.
\[ r = \frac{\text{Diameter}}{2} = \frac{28 \, \text{cm}}{2} = 14 \, \text{cm} \]

3. **Use the Formula for Curved Surface Area:**
- The formula for the curved surface area (CSA) of a right circular cylinder is:
\[ \text{CSA} = 2 \pi r h \]
where \( r \) is the radius and \( h \) is the height.

4. **Substitute the Values into the Formula:**
- Using \( \pi \approx \frac{22}{7} \):
\[ \text{CSA} = 2 \times \frac{22}{7} \times 14 \times 21 \]

5. **Calculate Step by Step:**
- First, calculate \( 2 \times \frac{22}{7} \):
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]
- Now, multiply by the radius:
\[ \frac{44}{7} \times 14 = \frac{44 \times 14}{7} = \frac{616}{7} \]
- Now, multiply by the height (21):
\[ \frac{616}{7} \times 21 = \frac{616 \times 21}{7} \]
- Simplifying \( \frac{616 \times 21}{7} \):
\[ 616 \div 7 = 88 \quad \text{(since 7 goes into 616 exactly 88 times)} \]
- Now multiply by 21:
\[ 88 \times 21 = 1848 \]

6. **Final Result:**
- Therefore, the curved surface area of the cylinder is:
\[ \text{CSA} = 1848 \, \text{cm}^2 \]