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To calculate the surface area of the semi-cylinder, we need to consider the different parts of its surface: the curved surface, the flat rectangular surface, and the two flat semi-circular ends.

### Given dataTo calculate the surface area of the semi-cylinder, we need to consider the different parts of its surface: the curved surface, the flat rectangular surface, and the two flat semi-circular ends.

### Given 
- Radius, \( r = 12.6 \, \text{cm} \)
- Height (length of the semi-cylinder), \( h = 20.1 \, \text{cm} \)

### Step 1: Calculate the curved surface area
The formula for the curved surface area of a full cylinder is \( 2\pi rh \). Since this is a semi-cylinder, we take half of that:
\[
\text{Curved Surface Area} = \pi r h = \pi (12.6)(20.1)
\]

### Step 2: Calculate the rectangular surface area
The rectangular surface forms the bottom of the semi-cylinder. Its length is the same as the height of the semi-cylinder, \( h = 20.1 \, \text{cm} \), and its width is the diameter of the semi-circle, \( 2r = 2 \times 12.6 = 25.2 \, \text{cm} \).
\[
\text{Rectangular Surface Area} = \text{width} \times \text{height} = 25.2 \times 20.1
\]

### Step 3: Calculate the surface area of the two semi-circular ends
The area of one semi-circle is:
\[
\text{Area of one semi-circle} = \frac{1}{2}\pi r^2 = \frac{1}{2} \pi (12.6)^2
\]
Since there are two such semi-circular ends:
\[
\text{Total area of semi-circular ends} = 2 \times \left(\frac{1}{2}\pi r^2 \right) = \pi r^2 = \pi (12.6)^2
\]

### Step 4: Total surface area
Now, we add all the calculated parts:
\[
\text{Total Surface Area} = \pi rh + 25.2 \times 20.1 + \pi r^2
\]

Let's calculate this.

The total surface area of the semi-cylinder is **1800.9 cm²**, correct to 1 decimal place.

Would you like more details or have any questions?

### Related Questions
1. How would the surface area change if the radius doubled while keeping the height the same?
2. What is the volume of this semi-cylinder?
3. How would you find the surface area of a full cylinder with the same dimensions?
4. How does the curved surface area compare with the flat surfaces in this problem?
5. How can we apply this surface area calculation in real-world scenarios?

### Tip
Always double-check unit conversions and formulas when working with different geometric shapes to avoid calculation errors.

A semi-cylinder has a radius of 12.6 cm and height of 20.1 cm. Work out the surface area of the semi-cylinder, correct to 1 decimal place.

This problem focuses on calculating the surface area of a semi-cylinder with a radius of 12.6 cm and height of 20.1 cm. Learn the steps using geometry formulas for cylindrical surfaces, applicable for Grades 9-11.

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