Which of false in case of a hollow cylinder. Write the correct answer.

Options

A. cuved surfacea area of a hollow cylinder`=2pih(R+r)`
B. Total surface area of a hollow cyloinder `2pi(R+r)(h+R+r)`
C. Inner cuved surface area of a hollow cylinder `=2pih(R-r)`
D. Area of each end of a hollow cylinder `=pi(R^(2)-r^(2))`

Answer

To determine which statements about a hollow cylinder are false, we need to analyze the properties and formulas related to a hollow cylinder. Let's go through the steps:

### Step-by-Step Solution:

1. **Define the Hollow Cylinder**:
- A hollow cylinder consists of two circular ends and a curved surface. It has an outer radius (R), an inner radius (r), and a height (h).

2. **Curved Surface Area (CSA)**:
- The curved surface area of a hollow cylinder is calculated using the formula:
\[ \text{Curved Surface Area} = 2\pi R h + 2\pi r h \]
- This can be simplified to:
\[ \text{Curved Surface Area} = 2\pi h (R + r) \]

3. **Total Surface Area (TSA)**:
- The total surface area of a hollow cylinder includes the curved surface area and the areas of the two circular ends:
\[ \text{Total Surface Area} = \text{Curved Surface Area} + \text{Area of the two ends} \]
- The area of the two ends is given by:
\[ \text{Area of the two ends} = 2 \times (\pi R^2 - \pi r^2) = 2\pi (R^2 - r^2) \]
- Therefore, the total surface area can be expressed as:
\[ \text{Total Surface Area} = 2\pi h (R + r) + 2\pi (R^2 - r^2) \]

4. **Volume of the Hollow Cylinder**:
- The volume of a hollow cylinder is calculated by subtracting the volume of the inner cylinder from the volume of the outer cylinder:
\[ \text{Volume} = \pi R^2 h - \pi r^2 h = \pi h (R^2 - r^2) \]

5. **Identify False Statements**:
- Now, we can check the options provided in the question (which are not specified here) against the formulas derived. Any statement that contradicts these formulas or definitions would be considered false.

### Conclusion:
To determine which statements are false, you would need to compare the provided options against the derived formulas for the hollow cylinder. Any incorrect formula or definition would be the false statement.