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The area of a square is equal to the area of a circle. Then the ratio between the side of the square and the radius of the circle is ______ .

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π : 1

1 : π

1 : π

answer is A.

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Detailed Solution

Here, we have been given that the area of a square and the area of a circle are equal. So, let us assume that the area of the square is

A 1

and that of the circle is

A 2

.
Thus we can say that:

A 1 = A 2 ................ (1)

Now, since we have to find the ratio of the side of the square and the radius of the circle, let us assume the side of the square to be ‘a’ units and the radius of the circle to be ‘r’ units. Thus, we have to find:

a : r

https://www.vedantu.com/question-sets/448c5db5-4e1f-4a23-a945-3b520ccb6da62248452249199419533.png

Now, we know that the area of a square with side ‘s’ is given as:
Area

= s 2

Here, s=a and area is

A 1

Thus we get:

A 1 = a 2

……………….(2)
Now, we also know that the area of a circle with radius ‘R’ is given as:
Area

= π r 2

Here, R = r and area is

A 2

. Thus we get:

A 2 = π r 2

………………….(3)
Now, if we put the value of

A 1

and

A 2

from equations (2) and (3) in equation (1) we will get:

A 1 = A 2 ⇒ a 2 = π r 2

Now, we know that we can transform this equation as:

a 2 = π r 2 ⇒ a 2 r 2 = π

Now, we can write it as:

a 2 r 2 = π ⇒ a r 2 = π

Now, taking under root both sides we get:

a r 2 = π ∴ a r = π

Thus, the ratio a:r is equal to

π : 1

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