The area of a circular playground is $22176\ m^2$. Find the cost of fencing this ground at the rate of Rs. 50 per metre.

Given:

The area of a circular playground is $22176\ m^2$.

Rate of fencing $=Rs.\ 50$ per metre.

To do:

We have to find the cost of fencing the ground.

Solution:

Let the radius of the circular playground be $r$.

We know that,

Circumference of a circle of radius $r=2 \pi r$

Area of a circle of radius $r=\pi r^2$

Therefore,

Area of the ground $=\frac{22}{7} \times (r)^2\ m^2$

$22176=\frac{22}{7}\times r^2$

$r^2=1008\times7\ m^2$

$r^2=7056\ m^2$

$r^2=(84)^2\ m^2$

$r=84\ m$

The circumference of the ground $=2 \pi (84)$

$=2\times \frac{22}{7} \times 84$

$=44\times12\ m$

$=528\ m$

The cost of fencing the ground $=Rs.\ 50\times528$

$=Rs.\ 26400$

The cost of fencing the ground is Rs. 26400.

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Updated on: 10-Oct-2022

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