Question

The area of two circles are in the ratio 1:2 if the two circles are bent in the form of squares , what is the ratio of their areas ?

Answer 1

$2\pi \: r \div 2\pi \: big \: r = 1by \: 2 \\ {s}^{2} by$

Answer 2

Answer:

1:2

Step-by-step explanation:

Let the radius of one circle be r and another circle be R

Area of circle=  $\pi r^2$

The area of two circles are in the ratio 1:2

So, $\frac{\pi r^2}{\pi R^2}=\frac{1}{2}$

$\frac{r^2}{R^2}=\frac{1}{2}$

$\frac{r}{R}=\frac{1}{\sqrt{2}}$ ---1

So circle perimeter equals square perimeter

Let a be the side of square made from circle of radius r and A be the square made from circle of radius R

$\frac{2\pi r}{2 \pi R}=\frac{4a}{4A}$

$\frac{r}{R}=\frac{4a}{4A}$

Using 1

$\frac{1}{\sqrt{2}}=\frac{a}{A}$

Now

$\frac{\text{Area of small square}}{\text{area of large square}}=\frac{a^2}{A^2}=(\frac{1}{\sqrt{2}})^2=\frac{1}{2}$

Thus the ratio of the area of squares is 1:2.