Question

The diameter of a circular pond is 17.5 m. It is surrounded by a 2 m wide path . Find the cost of constructing the path at the rate of $₹25per{m}^2$.

Answer 1

Given that a circular pond is surrounded by a wide path.
Diameter of circular pond = 17.5 m

$\therefore$ Radius of circular pond $\left(r_1\right)=\frac{Diameter}{2}$

i.e., $OA=r_1=\frac{17.5}{2}=8.75m$

Width of the path = 2 m

i.e., AB = 2 m

Now, length of $OB=OA+AB=r_1+AB$

Let $\left(r_e\right)=8.75+2=10.75m$

Area of circular path = Area of outer circle (circular pond + path) - Area of circular pond

$=\pi r_e^2-\pi r_1^2$

$=\pi (r_e^2-r_1^2)$

$=\pi \left\{\right(10.75{)}^2-\left(8.75{)}^2\right\}$

$=\pi \left\{\right(10.75+8.75\left)\right(10.75-8.75\left)\right\}$

$=122.46m^2$

Now, cost of constructing the path per square metre = ₹25

$\therefore$ Cost of constructing the path = Area of the path $\times$ Cost of constructing the path per square meter
= $₹122.46m^2=122.46\times 25$

$=₹3061.50$
Hence, required cost of constructing the path at the rate of $₹25per{m}^2$ is ₹3,061.