https://file.aiquickdraw.com/mathbot/file/172633201781137too2k9.jpg

รัศมี 5 ความสูง18.2
ให้ π เป็น22ส่วน7
ใช้สูตร2πrกำลัง2
กับ2πr

Based on the image, it appears to show a problem involving a cylinder with the following details:

- **Radius (รัศมี)**: \( r = 5 \, \text{cm} \)
- **Height (ความสูง)**: \( h = 18.2 \, \text{cm} \)
- **Value of \( \pi \)**: Given as \( \frac{22}{7} \)

You mentioned two formulas:
1. \( 2\pi r^2 \) – This could refer to the area of the two circular bases of the cylinder (each base has an area of \( \pi r^2 \), so two bases make \( 2\pi r^2 \)).
2. \( 2\pi rh \) – This is the formula for the lateral surface area of the cylinder (the area of the side surface).

### Calculations:

1. **Base Area**:
   \[
   A_{\text{base}} = \pi r^2 = \frac{22}{7} \times 5^2 = \frac{22}{7} \times 25 = \frac{550}{7} \approx 78.57 \, \text{cm}^2
   \]
   Since there are two bases:
   \[
   A_{\text{2 bases}} = 2 \times 78.57 = 157.14 \, \text{cm}^2
   \]

2. **Lateral Surface Area**:
   \[
   A_{\text{lateral}} = 2\pi rh = 2 \times \frac{22}{7} \times 5 \times 18.2 = \frac{220 \times 18.2}{7} = \frac{4004}{7} \approx 572 \, \text{cm}^2
   \]

3. **Total Surface Area** (including both the circular bases and the lateral surface):
   \[
   A_{\text{total}} = A_{\text{2 bases}} + A_{\text{lateral}} = 157.14 + 572 = 729.14 \, \text{cm}^2
   \]

Would you like more details on any step or further explanations? 

Here are some related questions:
1. How do we derive the formula for the surface area of a cylinder?
2. What happens to the surface area if the radius is doubled but the height remains the same?
3. How does the lateral surface area change when the height is increased by 50%?
4. How is the surface area of a cylinder related to its volume?
5. Can the same formulas be applied to other 3D shapes, like cones or spheres?

**Tip**: Always ensure to use the correct value of \( \pi \) (as given in the problem) for precise calculations.

รัศมี 5 ความสูง 18.2 ให้ π เป็น 22 ส่วน 7 ใช้สูตร 2πr^2 กับ 2πrh

Calculate the surface area of a cylinder with a radius of 5 cm and a height of 18.2 cm using π = 22/7. Learn the key formulas for both the circular base area and lateral surface area. Suitable for students in Grades 7-9.

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