Question

What is the radius of a wheel which covers a distance of 264 m in in 42 revolutions ?​

Answer 1

Step-by-step explanation:

$distance \: wheel \: cover \: in \: 42 \: revolution \: = \: 264m \\ distance \: it \: covers \: in \: 1 \: revolution \: = \: \frac{264}{42} = \frac{44}{7}$

the distance it covers in 1 revolution is actually the Circumference of the wheel.

therefore,

$2πr = Circumference$

$2πr = \frac{44}{7}$

$r = \frac{44}{7 \times 2π}$

$r = \frac{44}{14π} ≈1$

therefore radius of wheel is approx 1m.

it is approximately 1m means is not exactly 1m, it kind of look like this,

$\frac{44}{14π}=1.00040249943477068197584079834151884....$

Answer 2

Given:

distance covered by the wheel$=264 m$

Total revolutions$=42$

To find: radius of the wheel.

Solution:

Find the distance covered by the wheel in 1 revolution.

$\[\begin{array}{l} = \frac{{264}}{{42}}\\ = \frac{{44}}{7}\end{array}\]$

Understand that the distance of covered in 1 revolution is equation to the circumference of the wheel

Find the radius of the wheel.

$\[\begin{array}{l}C = 2\pi r\\ \Rightarrow \frac{{44}}{7} = 2 \times \frac{{22}}{7} \times r\\ \Rightarrow r = 1m\end{array}\]$

Hence, the radius of the wheel is 1 m.