Assume that the radius of the circle is 1.
The diagonal of the square is 2. By the Pythagorean Theorem, the side of the square of a right triangle will be 2/sqrt(2).
Finally, the ratio of the square to the circle, in area, will be
(2/sqrt(2))^2 : pi*(1)^2 = 2 : pi
We can conclude that the white area is about 35%.
Answer:
c
Step-by-step explanation:
120º is 1/3 of a complete revolution of 360º. So the area of this sector should be 1/3 the area of the complete circle.
A circle with radius 9 has area 9^2 π = 81π.
So the sector has area 81π/3.
Put another way: The area <em>A</em> of a circular sector and its central angle <em>θ</em> (in degrees) occur in the same ratio as the area of the entire circle with radius <em>r</em> according to
<em>A</em> / <em>θ </em>º = (π <em>r </em>^2) / 360º
==> <em>A</em> = π/360 <em>θ r</em> ^2
In this case, <em>r</em> = 9 and <em>θ</em> = 120º, so
<em>A</em> = π/360 * 120 * 81 = 81π/3
