Question

a wire is used to form a circular fence of radius 84cm which is then later converted into a square shaped fence by using the same length of wire.find the ratio of the area of the circuarl region to the area of the square region?​

Answer 1

Step-by-step explanation:

Radius of the circular fence, r= 84 cm.

So the length of circular fence,

$c = 2\pi \: r = 2 \times \frac{22}{7} \times 84$

$so \: \: c = 528$

So, Length of circular fence =528cm

Now the area of circular region

$a = \pi \: r {}^{2} = \frac{22}{7} \times 84 {}^{2}$

$so \: \: a = \frac{22}{7} \times 84 \times 84$

So, a= 22176 sq.cm

Perimeter square prepared =length of the fence

=528cm

So the side of the square = 528/4

= 132 cm

So the area of the square region = 132×132

=5544sqcm

Hence the required ratio = 22176 : 5544

= 22176/5544

=4/1

= 4:1