The radius of a wheel is 3.5 cm. What is the distance (in cm.) travelled by the wheel in 20 revolutions ?

Options

A. A)220
B. B)440
C. C)880
D. D)1320

Answer

To find the distance traveled by a wheel in a certain number of revolutions, we first need to 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 1: Calculate the circumference of the wheel
Given the radius \( r = 3.5 \) cm, we can substitute this value into the formula:

\[ C = 2 \pi (3.5) \]

Using \( \pi \approx 3.14 \):

\[ C = 2 \times 3.14 \times 3.5 \]

Calculating this step-by-step:

1. Calculate \( 2 \times 3.14 = 6.28 \)
2. Now multiply \( 6.28 \times 3.5 \):

\[ 6.28 \times 3.5 = 21.98 \text{ cm} \quad (\text{approximately}) \]

So, the circumference of the wheel is approximately \( 21.98 \) cm.

### Step 2: Calculate the distance traveled in 20 revolutions
Now, to find the distance traveled in 20 revolutions, we multiply the circumference by the number of revolutions:

\[ \text{Distance} = \text{Number of Revolutions} \times \text{Circumference} \]

Substituting the values we have:

\[ \text{Distance} = 20 \times 21.98 \]

Calculating this:

\[ 20 \times 21.98 = 439.6 \text{ cm} \quad (\text{approximately}) \]

### Final Answer
The distance traveled by the wheel in 20 revolutions is approximately \( 439.6 \) cm.