The‌ ‌circumference‌ ‌of‌ ‌the‌ ‌wheel‌ ‌of‌ ‌a‌ ‌cycle‌ ‌is‌ ‌2‌ ‌m‌ ‌20‌ ‌cm.‌ ‌How‌ ‌many‌ ‌revolutions‌ ‌will‌ ‌it‌ ‌take‌ ‌in‌ ‌covering‌ ‌16.83‌ ‌km?‌

Options

A. 9250
B. 7650
C. 8250
D. 10250

Answer

To solve the problem of how many revolutions the wheel of a cycle will take to cover 16.83 km, we can follow these steps:

### Step 1: Convert the circumference of the wheel into meters.
The circumference is given as 2 m 20 cm. We need to convert this entirely into meters.

1 meter (m) = 100 centimeters (cm)

So, 20 cm = 20/100 m = 0.2 m

Thus, the total circumference in meters is:
\[ 2 \, \text{m} + 0.2 \, \text{m} = 2.2 \, \text{m} \]

### Step 2: Convert the distance to be covered into meters.
The distance to be covered is given as 16.83 km. We need to convert this into meters.

1 kilometer (km) = 1000 meters (m)

So,
\[ 16.83 \, \text{km} = 16.83 \times 1000 \, \text{m} = 16830 \, \text{m} \]

### Step 3: Calculate the number of revolutions.
To find the number of revolutions, we can use the formula:
\[ \text{Number of Revolutions} = \frac{\text{Distance}}{\text{Circumference}} \]

Substituting the values we have:
\[ \text{Number of Revolutions} = \frac{16830 \, \text{m}}{2.2 \, \text{m}} \]

Calculating this gives:
\[ \text{Number of Revolutions} = 7645.45 \]

Since the number of revolutions must be a whole number, we round it down to 7645 revolutions.

### Final Answer:
The wheel will take approximately **7645 revolutions** to cover 16.83 km.

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