Question

A racing track is bounded by two concentric circles with circumferences 220 m and 286 m286 m. Calculate the area of the racing track.

Answer 1

We have,

Circumference of circle (1) $=220\text{m}$

Circumference of circle (2) $=286\text{m}$

Now,

In circle (1) :-

$2\pi r_1=220$

$\pi r_1=110$

$r_1=\frac{110}{\pi }$

$r_1=\frac{110}{\frac{22}{7}}$

$r_1=\frac{110\times 7}{22}$

$r_1=35\text{m}$

In circle (2) :-

$2\pi r_2=286$

$\pi r_2=143$

$r_2=\frac{143}{\pi }$

$r_2=\frac{143}{\frac{22}{7}}$

$r_2=\frac{143\times 7}{22}$

$r_2=45.5\text{m}$

So,

Area of racing track$=\pi ({r_2}^2-{r_1}^2)$

$=\frac{22}{7}[{\left(45.5\right)}^2-{\left(35\right)}^2]$

$=\frac{22}{7}[2070.25-1225]$

$=\frac{22}{7}\left[845.25\right]$

$=22\times 120.75$

$=2656.5{\text{m}}^2$

Hence, this is the answer.