What will be the ratio of the areas of a circle and a square, if the square is inscribed in the circle?

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π : 2

π : 4

π : 6

π : 8

answer is A.

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Detailed Solution

We have to find the ratio of the areas of a circle and a square, if the square is inscribed in the circle.
Constructing the figure,
Question Image

Suppose the side of the square is a and radius of the circle is r.
Note that, if a square is inscribed in a circle, then the diameter of the circle is equal to the diagonal of the square.

∴ 2 a = 2 r ⇒ a = 2 r

Calculating the ratio of areas of circle and square,

Area of circle= π r 2 Area of square=a 2 = 2 r 2 ⇒ R a t i o = π r 2 2 r 2 = π 2 = π : 2

So, the ratio of the areas of the circle and the square is

π : 2

.
Therefore, option 1 is correct.

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