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.

AAbout 25%
BAbout 40%
CAbout 60%
DAbout 50%

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 N class=

Verified Answer :

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

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

Answer:

about 60%

Step-by-step explanation:

just took the test