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

about 60%

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-(\pi r^2)/(3r^2\sqrt3)=1-(\pi)/(3\sqrt3)\approx0.395\approx40\%`