The radius of a wheel is 14 cm. What is the distance (in cm) travelled by the wheel in 15 revolutions ?

Options

A. 440
B. 660
C. 1320
D. 1980

Answer

To find the distance travelled by a wheel in 15 revolutions, we can follow these steps:

### Step 1: Calculate the Circumference of the Wheel
The formula for the circumference \( C \) of a circle (or wheel) is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius of the wheel.

### Step 2: Substitute the Radius
Given that the radius \( r \) is 14 cm, we can substitute this value into the formula:
\[ C = 2 \pi (14) \]

### Step 3: Use the Approximation for \( \pi \)
For calculations, we can use the approximation \( \pi \approx \frac{22}{7} \). Thus, we can rewrite the circumference as:
\[ C = 2 \times \frac{22}{7} \times 14 \]

### Step 4: Simplify the Calculation
Now, let's simplify the expression:
\[ C = \frac{44}{7} \times 14 \]
\[ C = \frac{44 \times 14}{7} \]
Calculating \( 44 \times 14 \):
\[ 44 \times 14 = 616 \]
So,
\[ C = \frac{616}{7} = 88 \text{ cm} \]

### Step 5: Calculate the Distance for 15 Revolutions
The distance travelled by the wheel in 15 revolutions is:
\[ \text{Distance} = \text{Number of Revolutions} \times \text{Circumference} \]
\[ \text{Distance} = 15 \times 88 \]

### Step 6: Perform the Final Calculation
Now, calculate \( 15 \times 88 \):
\[ 15 \times 88 = 1320 \text{ cm} \]

### Final Answer
The distance travelled by the wheel in 15 revolutions is:
\[ \text{Distance} = 1320 \text{ cm} \]

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