Question

The total cost of fencing a circular garden at the rate of$\$3$ per meter is$\$120\pi$ . Find the radius of the garden.
m

Answer 1

Given, the total cost of fencing $=\$120\pi$
Rate of fencing $=\$3$ per meter
As, the total cost of fencing is equal to the product of rate of fencing and length of the fence.
$\therefore \text{Length of the fence =}\frac{\text{Total cost of fencing}}{\text{Rate of fencing}}$
$=\frac{120\pi }{3}$
$=\frac{3\times 40\pi }{3}$
$=40\pi$

But, length of the fence is equal to the boundary length of the circle which is same as the circumference of the circle.


$\therefore$ Circumference of the circle $=40\pi$ m

The circumference of the circle is given by $C=2\pi r,$ where $r$ is the radius of the circle.
$\therefore 40\pi =2\pi \times r$
Divide both sides by $2\pi$
$\Rightarrow \frac{40\pi }{2\pi }=\frac{2\pi \times r}{2\pi }$
$\Rightarrow \frac{20\times 2\pi }{2\pi }=r$
$\Rightarrow 20=r$
$\Rightarrow r=20$ m

Hence, the radius of the circular garden is $20$ m.