The diameter of a wheel is 1.26 m. How far will it travel in 500 revolutions?
The diameter of the wheel is given as 1.26 m.
The circumference of a circle is given by the formula $C = \pi \times d$, where d is the diameter.
Circumference = $\pi \times 1.26$ meters.
The wheel makes 500 revolutions.
The total distance traveled is the distance per revolution multiplied by the number of revolutions.
Total distance = Circumference $\times$ Number of revolutions
Total distance = $(\pi \times 1.26) \times 500$ meters.
We can use the approximation $\pi \approx \frac{22}{7}$ or $\pi \approx 3.14$. Since the diameter 1.26 is divisible by 7 ($1.26 = 0.18 \times 7$), using $\pi \approx \frac{22}{7}$ will likely give a precise answer or one of the options.
$1.26 / 7 = 0.18$.
Total distance = $\frac{22}{7} \times 1.26 \times 500$
Total distance = $22 \times (1.26 / 7) \times 500$
Total distance = $22 \times 0.18 \times 500$
Total distance = $22 \times (0.18 \times 500)$
$0.18 \times 500 = 18 \times 5 = 90$.
Total distance = $22 \times 90$.
Total distance = $1980$ meters.
– Circumference of a circle = $\pi \times \text{diameter}$ or $2 \times \pi \times \text{radius}$.
– Total distance = Circumference $\times$ Number of revolutions.
Circumference $\approx 3.14 \times 1.26 \approx 3.9564$ m.
Total distance $\approx 3.9564 \times 500 \approx 1978.2$ m.
This is close to 1980 m, suggesting that 1980 m is the correct answer and the calculation with 22/7 was intended. The value 1.26 is specifically chosen to be a multiple of 0.07, making the use of $\pi = 22/7$ convenient.