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The image contains a problem asking to calculate the surface area of a solid shape, which is a cylinder capped with a cone on one side. Here’s how you can approach solving this problem:

### Given:
- **Cylinder**:
  - Radius \( r = 7 \, \text{cm} \)
  - Height \( h = 20 \, \text{cm} \)

- **Cone**:
  - Radius \( r = 7 \, \text{cm} \) (same as the cylinder)
  - Slant height \( l = 12 \, \text{cm} \)

### Formula for Surface Area:
1. **Surface Area of the Cylinder (excluding the base that attaches to the cone):**
   \[
   A_{\text{cylinder}} = 2\pi rh
   \]

2. **Surface Area of the Cone (excluding the base):**
   \[
   A_{\text{cone}} = \pi rl
   \]

3. **Total Surface Area:**
   \[
   A_{\text{total}} = A_{\text{cylinder}} + A_{\text{cone}} = 2\pi rh + \pi rl
   \]

### Calculations:
- For the cylinder:
  \[
  A_{\text{cylinder}} = 2\pi (7 \, \text{cm}) (20 \, \text{cm}) = 280\pi \, \text{cm}^2
  \]

- For the cone:
  \[
  A_{\text{cone}} = \pi (7 \, \text{cm}) (12 \, \text{cm}) = 84\pi \, \text{cm}^2
  \]

- **Total Surface Area**:
  \[
  A_{\text{total}} = 280\pi + 84\pi = 364\pi \, \text{cm}^2
  \]

  Since \(\pi \approx 3.14\):
  \[
  A_{\text{total}} \approx 364 \times 3.14 = 1143.76 \, \text{cm}^2
  \]

So, the surface area is approximately \( 1143.76 \, \text{cm}^2 \).

Would you like more details or have any questions?

### Related Questions:
1. How would the total surface area change if the height of the cylinder was increased?
2. What is the volume of the entire solid (cylinder + cone)?
3. How does changing the slant height of the cone affect the surface area?
4. Can you calculate the surface area if the cone was replaced with a hemisphere of the same radius?
5. What is the surface area of the cone alone?

### Tip:
Always check if the base area of the cylinder or cone needs to be included or excluded when calculating surface areas in composite shapes.

Calculate the surface area of a solid shape consisting of a cylinder with a height of 20 cm and a radius of 7 cm, capped with a cone with a slant height of 12 cm.

Learn how to calculate the surface area of a composite shape consisting of a cylinder with a height of 20 cm and a radius of 7 cm, capped with a cone with a slant height of 12 cm. This problem is suitable for students in Grades 9-11.

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