Which of these pipes will empty a pool the fastest ?
One pipe of diamater 60 cm
ii. Two pipes of diameter 30 cm each
iii Three pipes of diameter 20 cm each

Options

A. 1
B. 2
C. 3
D. None of these

Answer

To determine which of the pipes will empty a pool the fastest, we need to compare the flow rates of each pipe based on their diameters. The flow rate of a pipe is directly related to the cross-sectional area, which is determined by the diameter of the pipe.

### Step-by-Step Solution:

1. **Calculate the Cross-Sectional Area of Each Pipe:**
The formula for the cross-sectional area \( A \) of a pipe is given by:
\[ A = \pi r^2 \]
where \( r \) is the radius of the pipe.

2. **For the First Pipe (Diameter = 60 cm):**
- Radius \( r = \frac{60}{2} = 30 \) cm
- Area \( A_1 = \pi (30)^2 = \pi \times 900 = 900\pi \) cm²

3. **For the Second Option (Two Pipes, Diameter = 30 cm each):**
- Radius \( r = \frac{30}{2} = 15 \) cm
- Area of one pipe \( A_2 = \pi (15)^2 = \pi \times 225 = 225\pi \) cm²
- Since there are two pipes, total area \( A_{2\_total} = 2 \times 225\pi = 450\pi \) cm²

4. **For the Third Option (Three Pipes, Diameter = 20 cm each):**
- Radius \( r = \frac{20}{2} = 10 \) cm
- Area of one pipe \( A_3 = \pi (10)^2 = \pi \times 100 = 100\pi \) cm²
- Since there are three pipes, total area \( A_{3\_total} = 3 \times 100\pi = 300\pi \) cm²

5. **Compare the Areas:**
- Area of the first pipe: \( 900\pi \) cm²
- Area of the two pipes: \( 450\pi \) cm²
- Area of the three pipes: \( 300\pi \) cm²

6. **Conclusion:**
The first pipe with a diameter of 60 cm has the largest cross-sectional area and will therefore empty the pool the fastest.

### Final Answer:
The pipe with a diameter of 60 cm will empty the pool the fastest.