Question

If a square is inscribed in a circle find the ratio of the area of the circle and the square.

Answer 1

First, inscribed meaning inside of something.

first radius of the circle is r
then diagonal of the circle is equal to the diagonal of the square, means 2r

now length(l) of one side of the square is,
$l\sqrt{2} = 2r \\ l = 2r \div \sqrt{2} \\ l = r2 \sqrt{2} \div 2$
now area of the square should be,
${(r2 \sqrt{2} \div 2 )}^{2} \\ {r}^{2} 8 \div 4 \\ {r}^{2} 2$
now you know the area of a circle which is
$\pi {r}^{2}$
now ratio of them is,
r²2:πr²
2:π is the answer.


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Answer 2

Answer:

Step-by-step explanation:

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