The area of a hollow cylinder consists of two parts: the lateral surface area of the outer cylinder and the inner cylinder, as well as the areas of the two circular rings at the top and bottom.

### Given:
- Outer radius \( R \)
- Inner radius \( r \)
- Height \( h \)

### Surface Area Calculation:
1. **Lateral Surface Area**:
   - For the outer cylinder: \( A_{\text{outer}} = 2\pi R h \)
   - For the inner cylinder: \( A_{\text{inner}} = 2\pi r h \)

2. **Area of the Circular Rings** (top and bottom):
   - Area of a ring = Area of the outer circle − Area of the inner circle:
     \[
     A_{\text{ring}} = \pi (R^2 - r^2)
     \]
   - Since there are two rings (top and bottom), total ring area = \( 2 \times \pi (R^2 - r^2) \)

### Total Surface Area:
\[
A_{\text{total}} = 2\pi R h + 2\pi r h + 2\pi (R^2 - r^2)
\]
Simplifying:
\[
A_{\text{total}} = 2\pi h (R + r) + 2\pi (R^2 - r^2)
\]

This is the total surface area of the hollow cylinder.

Let me know if you'd like further details or clarifications!

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Here are 5 related questions to deepen your understanding:
1. How does the surface area formula change if the cylinder is open at one end?
2. What is the volume of a hollow cylinder?
3. How would you calculate the surface area of a cylinder with an elliptical base?
4. What if the height of the hollow cylinder is not given? Can you express the area in terms of the lateral surface area?
5. How does the surface area differ for a solid vs. a hollow cylinder?

**Tip:** Always ensure to double-check the units when calculating areas, especially when converting between different systems (e.g., cm² vs m²).

Learn how to calculate the surface area of a hollow cylinder, including its lateral surface areas and the areas of the circular rings at the top and bottom. This detailed guide covers key geometric formulas, such as 2πRh and 2π(R² - r²), and is suitable for students in Grades 9-12.

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