Question

The diameter of a wheel of a car is $70\text{cm}$. How much distance will it cover in $50$ revolutions?

• A. $350\text{m}$
• B. $110\text{m}$
• C. $165\text{m}$
• D. $220\text{m}$

Answer 1

The correct option is B

$110\text{m}$

• The perimeter of the circle is known as the circumference of the circle. The circumference $C$ of the circle with radis $r$ is given by $C=2\mathrm{\pi r}$.
• The distance covered by the wheel in one revolution will be equal to the circumference of the wheel.
• The diameter $d$ of the circle with radis $r$ is given by $d=2r$.

Step 1: Substitute $d=70$ into $d=2r$ and solve for $r$.

$\begin{array}{rcl}70& =& 2r\\ r& =& \frac{70}{2}\\ & =& 35\text{cm}\end{array}$

Step 2: Substitute $r=35$ into $C=2\mathrm{\pi r}$ and find the circumference of the wheel.

$\begin{array}{rcl}C& =& 2\times \frac{22}{7}\times 35\\ & =& 2\times 22\times 5\\ & =& 220\text{cm}\end{array}$

Step 3: The distance covered by the wheel in one revolution is $220\text{cm}$. Find the distance covered by the wheel in $50$ revolutions.

$\begin{array}{rcl}220\times 50& =& 11000\text{cm}\\ & =& \frac{11000}{100}\text{m}\\ & =& 110\text{m}\end{array}$

Hence, the correct option is $\mathit{b}$.