Question

The area of two circles are in the ratio of 1:2. If two circles are bent in the form of squares , what is the ratio of their areas ?
A. 1:2
B. 1:4
C. 1:√2
D. 1:3

Answer 1

1:2 only,as area is square of the side of a square.,let it be r.then as circle area is in the ratio 1:2 ,the same follows here.

Answer 2

Answer:

A. 1:2

Step-by-step explanation:

Let $r_1$ be the radius of one circle,

⇒ its circumference = $2\pi(r_1)$

After making a square from this circle,

The perimeter of the square will be same as the circumference of the circle,

⇒ The perimeter of the square formed by first circle = $2\pi(r_1)$

⇒ 4 × Side of the square formed by first circle = $2\pi(r_1)$

⇒ Side of the square formed by first circle = $\frac{2\pi(r_1)}{4}=\frac{\pi r_1}{2}$

⇒ Area of the square formed by first circle = $(\frac{\pi r_1}{2})^2=\frac{\pi^2 r_1^2}{4}$

Now, if $r_2$ be the radius of second circle,

Similarly,

Area of the square formed by second circle = $\frac{\pi^2 r_2^2}{4}$

Given,

$\frac{\pi (r_1)^2}{\pi (r_2)^2}=\frac{1}{2}$

$\implies \frac{(r_1)^2}{(r_2)^2}=\frac{1}{2}$

Hence, the ratio of the area of squares formed by first and second circles

$=\frac{\frac{\pi^2 r_1^2}{4}}{\frac{\pi^2 r_2^2}{4}}$

$=\frac{r_1^2}{r^2}$

$=\frac{1}{2}$