In the shortcut method for calculating circle area from a square, the circle area equals the square area multiplied by what factor?

In the shortcut method for calculating circle area from a square, the circle area equals the square area multiplied by what factor?

• A. 0.785
• B. 0.92
• C. 0.65
• D. 1.000

Answer: (A)

The shortcut relies on the ratio between the area of a circle and the area of a square when the circle is inscribed in the square (the circle’s diameter equals the square’s side). Circle area is πr^2, and with diameter equal to the square side s, the radius is r = s/2. This makes the circle’s area π(s/2)^2 = πs^2/4. The square’s area is s^2, so the circle’s area is (π/4) times the square’s area. Since π/4 ≈ 0.785, you multiply the square area by about 0.785 to get the circle area. The other numbers don’t match this ratio (0.92 and 0.65 would come from different relationships, and 1.000 would imply equal areas).

The shortcut relies on the ratio between the area of a circle and the area of a square when the circle is inscribed in the square (the circle’s diameter equals the square’s side). Circle area is πr^2, and with diameter equal to the square side s, the radius is r = s/2. This makes the circle’s area π(s/2)^2 = πs^2/4. The square’s area is s^2, so the circle’s area is (π/4) times the square’s area. Since π/4 ≈ 0.785, you multiply the square area by about 0.785 to get the circle area. The other numbers don’t match this ratio (0.92 and 0.65 would come from different relationships, and 1.000 would imply equal areas).