Question 6

The distance covered in one revolution of a tyre is its circumference.

Step 1 — Calculate distance in one revolution

First, we find the radius of the tyre. The diameter is 56 cm. So, the radius is half of the diameter.

$r = \frac{\text{diameter}}{2}$

$r = \frac{56}{2}$

$r = 28 \text{ cm}$

Now, we calculate the circumference. We use the formula $C = 2\pi r$. We will use $\pi = \frac{22}{7}$.

$C = 2 \times \frac{22}{7} \times 28$

$C = 2 \times 22 \times 4$

$C = 44 \times 4$

$\boxed{176 \text{ cm}}$

Step 2 — Calculate number of revolutions

The car travels a total distance of 10 km. We need to convert this distance to centimeters. We know that $1 \text{ km} = 1000 \text{ m}$. Also, $1 \text{ m} = 100 \text{ cm}$.

$\text{Total distance} = 10 \times 1000 \times 100 \text{ cm}$

$\text{Total distance} = 1,000,000 \text{ cm}$

Now, we find the number of revolutions. We divide the total distance by the distance per revolution.

$\text{Number of revolutions} = \frac{\text{Total distance}}{\text{Distance per revolution}}$

$\text{Number of revolutions} = \frac{1,000,000}{176}$

$\text{Number of revolutions} \approx 5681.82$

We round this to the nearest whole number.

$\boxed{5682 \text{ revolutions}}$

Answer

(i) The car travels 176 cm in one revolution. (ii) The tyre makes approximately 5682 revolutions.