An artist wishes to paint a circular region on a square poster that is 2 feet on a side. If the area of the circular region is to be 1/2 the area of the poster, what must be the radius of the circular region in feet?
$$A.\ \frac{1}{\pi}$$
$$B.\ \sqrt{\frac{2}{\pi}}$$
$$C.\ 1$$
$$D.\ \frac{2}{\sqrt{\pi}}$$
$$E.\ \frac{\pi}{2}$$
The OA is B.
If the square has a side of 2 feet, that's mean that its area is 2 x 2 = 4.
1/2 * area the of square is = 2.
Then, we know that the area of a circle is defined as,
$$\pi\cdot r^2$$
and it should be equal 2
$$\pi\cdot r^2=2$$
$$\pi\cdot r^2=2\Rightarrow \ r^2=\frac{2}{\pi}\Rightarrow \ r=\sqrt{\frac{2}{\pi}}$$
Option B.
Experts, is there another approach to solve this PS question? Thanks!
$$A.\ \frac{1}{\pi}$$
$$B.\ \sqrt{\frac{2}{\pi}}$$
$$C.\ 1$$
$$D.\ \frac{2}{\sqrt{\pi}}$$
$$E.\ \frac{\pi}{2}$$
The OA is B.
If the square has a side of 2 feet, that's mean that its area is 2 x 2 = 4.
1/2 * area the of square is = 2.
Then, we know that the area of a circle is defined as,
$$\pi\cdot r^2$$
and it should be equal 2
$$\pi\cdot r^2=2$$
$$\pi\cdot r^2=2\Rightarrow \ r^2=\frac{2}{\pi}\Rightarrow \ r=\sqrt{\frac{2}{\pi}}$$
Option B.
Experts, is there another approach to solve this PS question? Thanks!
