A diameter PQ is drawn to a circle whose diameter length is 1 m. A square is drawn using the diameter PQ as one of its sides. Assuming that w is 22/7, what is the area of the part of the square lying outside the circle ?

Given that the diameter of the circle (PQ) is 1 m, its radius (r) is 0.5 m. A square is constructed with PQ as one of its sides, meaning the side of the square (s) is 1 m. The area of the square is s² = 1² = 1 sq. m.

Since PQ is both a side of the square and the diameter of the circle, the center of the circle lies at the midpoint of side PQ. Consequently, exactly half of the circle (a semicircle) lies within the boundaries of the square. The area of this semicircle is ¹⁄₂ × πr².

Using π (denoted as 'w' in the question) ≈ 22/7 and r = 1/2 m:
Area of semicircle = ¹⁄₂ × (22/7) × (1/2)² = ¹⁄₂ × 22/7 × 1/4 = 11/28 sq. m.

The area of the part of the square lying outside the circle is:
Area of Square - Area of semicircle = 1 - 11/28 = 17/28 sq. m.