Find the total surface area of a cylinder with radius 21 cm and height 5 cm.

Answer

To find the total surface area (TSA) of a cylinder with a radius of 21 cm and a height of 5 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Total Surface Area of a Cylinder**:
The formula for the total surface area (TSA) of a cylinder is given by:
\[ \text{TSA} = 2\pi r (r + h) \]
where \( r \) is the radius and \( h \) is the height of the cylinder.

2. **Identify the Given Values**:
From the problem, we have:
- Radius \( r = 21 \) cm
- Height \( h = 5 \) cm

3. **Substitute the Values into the Formula**:
Now, we substitute the values of \( r \) and \( h \) into the TSA formula:
\[ \text{TSA} = 2 \pi (21) (21 + 5) \]

4. **Calculate the Sum Inside the Bracket**:
First, calculate \( r + h \):
\[ 21 + 5 = 26 \]
Now, substitute this back into the formula:
\[ \text{TSA} = 2 \pi (21) (26) \]

5. **Use Approximation for \(\pi\)**:
We can use \( \pi \approx \frac{22}{7} \) for our calculations:
\[ \text{TSA} = 2 \times \frac{22}{7} \times 21 \times 26 \]

6. **Calculate Step by Step**:
- First calculate \( 2 \times \frac{22}{7} = \frac{44}{7} \)
- Now calculate \( 21 \times 26 = 546 \)
- So, we have:
\[ \text{TSA} = \frac{44}{7} \times 546 \]

7. **Multiply and Simplify**:
- Now, multiply \( 44 \times 546 \):
\[ 44 \times 546 = 24024 \]
- Now divide by 7:
\[ \text{TSA} = \frac{24024}{7} = 3432 \text{ cm}^2 \]

8. **Conclusion**:
Therefore, the total surface area of the cylinder is:
\[ \text{TSA} = 3432 \text{ cm}^2 \]