Question

A circle touches all the sides of a square then will the circle equal to square

Answer 1

Answer:

Let the circle have radius  r  units. Then the outer square would have its sides equal to the diameter of the circle, i.e.  2r  units. The inner square would have its diagonals equal to the diameter of the circle. By Pythagoras' Theorem, the sides of the inner square would thus be  r2–√  units long.

The total area of the 4 spaces between the inner square and the circle is thus  πr2−(r2–√)2=πr2−2r2=(π−2)r2 .

The total area of the four spaces between the circle and the outer square is  (2r)2−πr2=4r2−πr2=(4−π)r2 .

Since  4−π≈0.8584  and  π−2≈1.1416 , the answer is no. Indeed, we can say more: the total area of the 4 spaces between the inner square and the circle will always be larger than the total area of the four spaces between the circle and the outer square, no matter how large or small the radius of the circle is.

Step-by-step explanation:

Answer 2

Answer:

A circle touches all the sides of a square then will the circle equal to square

no , the circle would not be equal to the square on touching its edges

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