Question

If a square is inscribed in a circle, find 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:

SOLUTION :  

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

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

$\huge \mathbb{Answer}$

=>7 : 11

$\bold{Step \: by \: step \: explaination}$

Let side of square be 'a'

Area of square is a²

Diagonal of sqare is √{a²+a²}

Or √2a

So diameter of circle is equal to diagonal of sqare.

Then diameter=√2a

Radius(r)=√2a/2

=a/√2

Area of circle=πr²

=π{a/√2}²

=πa²/2

Ratio of area of square and area of circle =

a²:πa²/2

=1:π/2

=2:π

=2:22/7

=14:22

=7:11