Calculating Wheel Revolutions Based on Radius and Distance

The question asks us to find out how many revolutions a wheel with a radius of 35 cm will make to cover a total distance of 11 km.

To solve this, we first need to understand what distance a wheel covers in one revolution. The distance covered in one complete revolution of a wheel is equal to its circumference.

The formula for the circumference of a circle is given by:

$\text{Circumference} (C) = 2\pi r$

where $r$ is the radius of the wheel and $\pi$ is a mathematical constant, approximately equal to $\frac{22}{7}$ or 3.14.

Given:

• Radius of the wheel ($r$) = 35 cm
• Total distance to be covered = 11 km

We need to ensure the units are consistent. Let's convert both measurements to the same unit, for instance, metres.

• Convert radius from cm to m: $35 \text{ cm} = 35 / 100 \text{ m} = 0.35 \text{ m}$
• Convert total distance from km to m: $11 \text{ km} = 11 \times 1000 \text{ m} = 11000 \text{ m}$

Now, let's calculate the circumference of the wheel using the radius in metres. We can use the value of $\pi = \frac{22}{7}$ because the radius (35 cm or 0.35 m) is a multiple of 7.

$C = 2 \times \frac{22}{7} \times 0.35 \text{ m}$

We can calculate this:

$C = 2 \times \frac{22}{7} \times \frac{35}{100} \text{ m}$

$C = 2 \times 22 \times \frac{5}{100} \text{ m}$

$C = 44 \times \frac{1}{20} \text{ m}$

$C = \frac{44}{20} \text{ m}$

$C = 2.2 \text{ m}$

So, the wheel covers a distance of 2.2 metres in one revolution.

To find the total number of revolutions required to cover 11 km (or 11000 m), we divide the total distance by the distance covered in one revolution:

$\text{Number of Revolutions} = \frac{\text{Total Distance}}{\text{Circumference}}$

$\text{Number of Revolutions} = \frac{11000 \text{ m}}{2.2 \text{ m}}$

Now, we perform the division:

$\text{Number of Revolutions} = \frac{11000}{2.2} = \frac{110000}{22}$

$\text{Number of Revolutions} = 5000$

Therefore, the wheel will make 5000 revolutions to cover a distance of 11 km.

Let's look at the given options:

Our calculated number of revolutions is 5000, which matches option 3.

In summary, calculating the circumference and dividing the total distance by the circumference gives us the number of revolutions the wheel makes.