Question

The ratio of the outer and inner circumference of a circular path as shown in the figure is $36:25$. If the path is $5m$ wide, then find :
(i) the area enclosed by the path
(ii) the diameter of the inner circle

Answer 1

Let the radius of outer and inner circle be $R$ and $r$ respectievly.

According to the given condition,

$\frac{2\pi R}{2\pi r}=\frac{36}{25}$

$25R=36r$

$⟹R=\frac{36r}{25}$

Width of the path is given as $5$ m which is equal to $R-r$.

$R-r=5$

So, $\frac{36r}{25}-r=5\Rightarrow \frac{11r}{25}=5\Rightarrow r=\frac{125}{11}$m

And $R=\frac{36r}{25}=\frac{36\times 125}{25\times 11}=\frac{180}{11}$m

Area of path$=\pi (R^2-r^2)=\frac{22}{7}\times \frac{1}{121}({\left(180\right)}^2-{\left(125\right)}^2)$

Area of path$=435.71m^2$

Diameter of inner circle$=2r=\frac{250}{11}$m