i have a circle in a square the area of the circle is 81 cm2 find the diaginal of the square

Question

circle is inscribed in the square touches each side of the square

Answer 1

If the circle touches each side of the square (at the middle of each edge), then the diameter of the circle is the same length as a side of the square.  We can use the Pythagorean Theorem to determine the length of the diagonal of the square, but it is good to remember a set of "Pythagorean Triples" -- n*1, n*1, n*SQRT(2); these are the sides of a 45°-45°-90° triangle (half of the square)

 

The area of the circle is: 81 cm² = ∏r² = ∏(d/2)²                  (note that radius = diameter/2)

                           (81)*(4/∏) = d²

                             d = SQRT(324/∏)

 

Now, the diagonal of the square (call it x) is:    SQRT(324/∏)*SQRT(2)

                                                   x = SQRT(648/∏)

                                                   x ≈ 14.36 cm

 

Answer 2

A = πr²

81 = πr²

25.7831 ≈ r²

5.0777 ≈ r

 

The diagonal is the same length as the twice the radius, 10.155 cm