Find the curved surface area (in `"cm"^2`) of a right circular cylinder of diameter 28 cm and height 12 cm.

Options

A. 968
B. 924
C. 856
D. 1056

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 cylinder = 28 cm
- Height of the cylinder = 12 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 the curved surface area of a cylinder**:
- 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**:
- Here, we can use \( \pi \approx \frac{22}{7} \) for calculation.
\[ \text{CSA} = 2 \times \frac{22}{7} \times 14 \, \text{cm} \times 12 \, \text{cm} \]

5. **Calculate the CSA**:
- First, calculate \( 2 \times 14 \):
\[ 2 \times 14 = 28 \]
- Now substitute back into the equation:
\[ \text{CSA} = \frac{22}{7} \times 28 \times 12 \]
- Next, simplify \( \frac{28}{7} \):
\[ \frac{28}{7} = 4 \]
- Now, continue with the calculation:
\[ \text{CSA} = 22 \times 4 \times 12 \]
- Calculate \( 22 \times 4 \):
\[ 22 \times 4 = 88 \]
- Now multiply by 12:
\[ 88 \times 12 = 1056 \]

6. **Final Result**:
- Therefore, the curved surface area of the cylinder is:
\[ \text{CSA} = 1056 \, \text{cm}^2 \]