Question

A circular pond is 17.5 m is of diameter. It is surrounded by a 2m wide path . Find the cost of constructing the path at the rate of $₹25per{m}^2$. [4 Marks]

Answer 1

[1 Mark]

Given that a circular pond is surrounded by a wide path.

The diameter of circular pond $=17.5m$

$\therefore$ 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, $AB=2m$
$OB=OA+AB$
$=r_1+AB$

Let $\left(r_e\right)=8.75+2=10.75m$ [1 Mark]

So, area of circular path $=$ Area of outer circle $-$ Area of circular pond

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

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

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

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

$=122.46m^2$ [1 mark]

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 $=122.46\times 25$

$=₹3061.50$ [1 mark]

Hence, required cost of constructing the path at the rate of $₹25per{m}^2$ is $₹3061$.