Question

a square is inscribes in a circle. find the ratio of their areas

Answer 1

So side of square be 'a'

Ans Area of square is a²

Diagonal of square is √{a²+a²}

Or √2a

So diameter of circle is equal to diagonal of square .

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

Answer 2

When a square inscribed in a circle then,

Diameter of circle = diagonal of square

Let side of the square be = a cm

Diagonal of square be =

$\sqrt{2a} cm$

.

Area of square =

${a}^{2} {cm}^{2}$

.

Diameter of circle =

$\sqrt{2} a \: cm$

.

؞ radius of circle =

$\frac{ \sqrt{2} a}{2}= \: \frac{ \sqrt{a} }{2}$

Area of circle =

$\frac{π \: \: {a}^{2} }{2}$

.

Ratio of area of circle and square =

$\frac{π \:{a}^{2} }{2} : \: {a}^{2}$

$\large \boxed{π:2}$

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