Which is false? Write the correct answer.

Options

A. Volume of the hollow sphere`=(4)/(3)pi(R^(3)-r^(3))`
B. Volume of a hemisphere`=(2)/(3)pir^(3)`
C. Total surface area of a hemisphere`=3pir^(2)`
D. Curved surface area of a hemisphere`=pir^(2)`

Answer

To determine which statement is false among the given options regarding the properties of a hemisphere, we will analyze each option step by step.

### Step 1: Analyze Option A
- **Statement**: Volume of a hemisphere is given as \( \frac{4}{3} \pi r^3 - r^3 \).
- **Correct Calculation**: The volume of a hemisphere is actually \( \frac{2}{3} \pi r^3 \) (half of the volume of a sphere, which is \( \frac{4}{3} \pi r^3 \)).
- **Conclusion**: This statement is incorrect.

### Step 2: Analyze Option B
- **Statement**: Volume of a hemisphere is \( \frac{2}{3} \pi r^3 \).
- **Correct Calculation**: This is indeed the correct formula for the volume of a hemisphere.
- **Conclusion**: This statement is correct.

### Step 3: Analyze Option C
- **Statement**: Total surface area of a hemisphere is \( 3\pi r^2 \).
- **Correct Calculation**: The total surface area of a hemisphere includes the curved surface area (which is \( 2\pi r^2 \)) and the base area (which is \( \pi r^2 \)). Thus, the total surface area is \( 2\pi r^2 + \pi r^2 = 3\pi r^2 \).
- **Conclusion**: This statement is correct.

### Step 4: Analyze Option D
- **Statement**: Curved surface area of a hemisphere is \( \pi r^2 \).
- **Correct Calculation**: The curved surface area of a hemisphere is actually \( 2\pi r^2 \) (half of the surface area of a sphere, which is \( 4\pi r^2 \)).
- **Conclusion**: This statement is incorrect.

### Final Conclusion
- **False Statement**: The incorrect statement is found in Option D, where it states that the curved surface area of a hemisphere is \( \pi r^2 \). The correct answer is \( 2\pi r^2 \).

### Summary of Findings
- **Option A**: Incorrect (correct volume is \( \frac{2}{3} \pi r^3 \))
- **Option B**: Correct (volume is \( \frac{2}{3} \pi r^3 \))
- **Option C**: Correct (total surface area is \( 3\pi r^2 \))
- **Option D**: Incorrect (correct curved surface area is \( 2\pi r^2 \))