The radius of a circular wheel is 42 cm. Find the distance travelled by it in:
(i) 1 revolution
(ii) 50 revolutions
(iii) 200 revolutions

Answer

To solve the problem step by step, we will find the distance traveled by a circular wheel with a radius of 42 cm in one revolution, 50 revolutions, and 200 revolutions.

### Step 1: Calculate the Circumference of the Wheel
The distance traveled in one revolution is equal to the circumference of the wheel. The formula for the circumference \( C \) of a circle is given by:

\[ C = 2 \pi r \]

Where:
- \( r \) is the radius of the circle.
- \( \pi \) is approximately \( \frac{22}{7} \) or \( 3.14 \).

Given:
- Radius \( r = 42 \) cm.

Substituting the value of \( r \):

\[ C = 2 \times \frac{22}{7} \times 42 \]

### Step 2: Simplify the Calculation
First, calculate \( 2 \times 42 \):

\[ 2 \times 42 = 84 \]

Now substitute this back into the equation:

\[ C = \frac{22}{7} \times 84 \]

Now simplify \( \frac{84}{7} \):

\[ \frac{84}{7} = 12 \]

Now multiply by 22:

\[ C = 22 \times 12 = 264 \text{ cm} \]

### Step 3: Distance Traveled in 1 Revolution
The distance traveled in one revolution is equal to the circumference:

\[ \text{Distance in 1 revolution} = C = 264 \text{ cm} \]

### Step 4: Distance Traveled in 50 Revolutions
To find the distance traveled in 50 revolutions, multiply the circumference by 50:

\[ \text{Distance in 50 revolutions} = 50 \times C = 50 \times 264 \]

Calculating this:

\[ 50 \times 264 = 13200 \text{ cm} \]

### Step 5: Distance Traveled in 200 Revolutions
To find the distance traveled in 200 revolutions, multiply the circumference by 200:

\[ \text{Distance in 200 revolutions} = 200 \times C = 200 \times 264 \]

Calculating this:

\[ 200 \times 264 = 52800 \text{ cm} \]

### Final Answers
- Distance traveled in 1 revolution: **264 cm**
- Distance traveled in 50 revolutions: **13200 cm**
- Distance traveled in 200 revolutions: **52800 cm**

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