The diameter of a cylinder is 28 cm and its height is 20 cm . The total surface area of the cylinder is

Options

A. `2993 cm^2`
B. `2992 cm^2`
C. 2292 `cm^2`
D. 2229 `cm^2`

Explanation

To find the total surface area of a cylinder, we can use the formula:

\[ \text{Total Surface Area} = 2\pi r(h + r) \]

where \( r \) is the radius and \( h \) is the height of the cylinder.

### Step-by-Step Solution:

1. **Identify the given values**:
- Diameter of the cylinder = 28 cm
- Height of the cylinder (h) = 20 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. **Substitute the values into the formula**:
- Now we have \( r = 14 \text{ cm} \) and \( h = 20 \text{ cm} \).
\[ \text{Total Surface Area} = 2\pi r(h + r) = 2\pi \times 14 \times (20 + 14) \]

4. **Calculate \( h + r \)**:
\[ h + r = 20 + 14 = 34 \text{ cm} \]

5. **Substitute \( h + r \) back into the formula**:
\[ \text{Total Surface Area} = 2\pi \times 14 \times 34 \]

6. **Calculate \( 2 \times 14 \)**:
\[ 2 \times 14 = 28 \]

7. **Now calculate \( 28 \times 34 \)**:
\[ 28 \times 34 = 952 \]

8. **Finally, multiply by \( \pi \)** (using \( \pi \approx \frac{22}{7} \)):
\[ \text{Total Surface Area} = 952 \times \frac{22}{7} \]

9. **Calculate \( 952 \times \frac{22}{7} \)**:
\[ = \frac{952 \times 22}{7} = \frac{20944}{7} \approx 2992 \text{ cm}^2 \]

### Final Answer:
The total surface area of the cylinder is approximately \( 2992 \text{ cm}^2 \).