A bucket is drawn from a well by means of a rope which is wound around a wheel of radius 48 cm. If the bucket ascends in 1 minute 12 seconds at a speed of 1.2 m/sec. find the length of the rope.

Options

A. 8.64 cm
B. 86.4 cm
C. 864 cm
D. 8640 cm

Answer

To solve the problem, we need to find the length of the rope used to draw the bucket from the well. Let's break it down step by step:

### Step 1: Convert the time from minutes and seconds to seconds
The time given is 1 minute and 12 seconds. We need to convert this into seconds.

- **Calculation**:
\[ \text{Total time in seconds} = 1 \text{ minute} \times 60 \text{ seconds/minute} + 12 \text{ seconds} = 60 + 12 = 72 \text{ seconds} \]

### Step 2: Calculate the distance the bucket ascends
The speed of the bucket is given as 1.2 m/s. To find the distance the bucket ascends in the given time, we use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

- **Calculation**:
\[ \text{Distance} = 1.2 \text{ m/s} \times 72 \text{ s} = 86.4 \text{ meters} \]

### Step 3: Convert the distance from meters to centimeters
Since the final answer needs to be in centimeters, we convert the distance from meters to centimeters. We know that 1 meter = 100 centimeters.

- **Calculation**:
\[ \text{Distance in centimeters} = 86.4 \text{ meters} \times 100 \text{ cm/m} = 8640 \text{ cm} \]

### Conclusion
The length of the rope used to draw the bucket from the well is **8640 cm**.