In the shortcut method, the area of the circle is obtained by multiplying the area of the bounding square by what factor?

In the shortcut method, the area of the circle is obtained by multiplying the area of the bounding square by what factor?

• A. 0.5
• B. 1.0
• C. 0.785
• D. 1.25

Answer: (C)

When you use the shortcut method, the circle sits inside a bounding square with the circle’s diameter equal to the square’s side. If the square’s area is s^2, the circle’s area is pi (s/2)^2 = (pi/4) s^2. That means the circle’s area is pi/4 times the square’s area. Since pi/4 ≈ 0.785, multiplying the square’s area by 0.785 gives the circle’s area.

When you use the shortcut method, the circle sits inside a bounding square with the circle’s diameter equal to the square’s side. If the square’s area is s^2, the circle’s area is pi (s/2)^2 = (pi/4) s^2. That means the circle’s area is pi/4 times the square’s area. Since pi/4 ≈ 0.785, multiplying the square’s area by 0.785 gives the circle’s area.