Diameter of a wheel is 3 cm. The wheel revolves 28 times in a minute. To cover 5.280 km distance, the wheel will take (Take `pi = (22)/(7)`) :

Options

A. 10 minutes
B. 20 minutes
C. 30 minutes
D. 40 minutes

Answer

To solve the problem step by step, we need to find out how long it takes for a wheel with a diameter of 3 cm to cover a distance of 5.280 km when it revolves 28 times in a minute. We'll use the formula for the circumference of a circle and some unit conversions.

### Step 1: Convert the distance from kilometers to centimeters.
1 kilometer = 1000 meters
1 meter = 100 centimeters
Therefore, 5.280 km = 5.280 × 1000 × 100 = 528000 cm.

**Hint:** Always convert all measurements to the same unit for consistency.

### Step 2: Calculate the radius of the wheel.
The diameter of the wheel is given as 3 cm.
Radius (r) = Diameter / 2 = 3 cm / 2 = 1.5 cm.

**Hint:** The radius is half of the diameter.

### Step 3: Calculate the circumference of the wheel.
Circumference (C) = 2 × π × r.
Using π = 22/7, we have:
C = 2 × (22/7) × 1.5 cm
C = (44/7) × 1.5 cm
C = (44 × 1.5) / 7 cm
C = 66 / 7 cm ≈ 9.43 cm.

**Hint:** The circumference is the distance the wheel travels in one complete revolution.

### Step 4: Calculate the distance traveled in one minute.
The wheel revolves 28 times in one minute, so the distance traveled in one minute (D) is:
D = Circumference × Number of revolutions
D = (66/7) cm × 28
D = (66 × 28) / 7 cm
D = 1848 / 7 cm ≈ 264 cm.

**Hint:** Multiply the circumference by the number of revolutions to find the total distance traveled in that time.

### Step 5: Calculate the time taken to cover 528000 cm.
Let T be the time in minutes to cover 528000 cm.
Using the formula:
Distance = Speed × Time, we can rearrange it to find time:
T = Distance / Speed
T = 528000 cm / (264 cm/min).

**Hint:** To find time, divide the total distance by the distance covered per minute.

### Step 6: Calculate T.
T = 528000 / 264 = 2000 minutes.

**Hint:** Perform the division carefully to ensure accuracy.

### Final Answer:
The wheel will take 2000 minutes to cover a distance of 5.280 km.