Question

If a square is inscribed in a circle, what is the ratio of the areas of the circle and the square?

Answer 1

Answer:

The ratio of the areas of the circle and the square is π : 2.

Step-by-step explanation:

Given :  

A square inscribed in a circle .Then  

Diameter of circle = diagonal of square

Let side of the square be ‘a’ cm.

Diameter of circle = Diagonal of square  =√2a

Diameter of circle = √2a

Radius of the circle ,r  = Diameter of circle/2  

r = √2a/2 cm

Radius of the circle ,r = √2a/2 cm

Area of circle , A1 = πr²  

A1 = π(√2a/2)² = π × 2a²/4 = π×a²/2

A1 = πa²/2

Area of square, A2 = a²

Ratio of area of circle and square = A1 : A2 =  πa²/2 : a²

= πa² : 2a²

= π : 2

A1 : A2 = π : 2

Hence, the ratio of the areas of the circle and the square is π : 2.

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Answer 2

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