Question

A circle is inscribed in an equilateral triangle. A point in the figure is selected at random. Find the probability that the point will be in the part that is NOT shaded.
A. About 25%
B. About 40%
C. About 60%
D. About 50%

Answer 1

Answer:

about 60%

Step-by-step explanation:

just took the test

Answer 2

If $r$ is the radius of the circle, then the side length of the triangle is $2r\sqrt3$.

The area of the circle is $\pi r^2$, while the area of the triangle is $3r^2\sqrt3$.

So, the probability of selecting a random point in the white space is

$1-\dfrac{\pi r^2}{3r^2\sqrt3}=1-\dfrac{\pi}{3\sqrt3}\approx0.395\approx40\%$