Area of base is a circle = 4√3
Probability of the grain of sand landing on the portion of the base outside the triangle is 3/4, so probability of the grain of sand landing on the portion of the base inside the triangle is 1/4.
So, area of equilateral triangle = (1/4)(Area of circle) = √3

If a is the side of equilateral triangle, area of equilateral triangle = (1/2)(base)(height) = (1/2)(a)(a√3/2) = (a^2)(√3/4)
We earlier found that area of equilateral triangle = √3, so (a^2)(√3/4) = √3, which implies a^2 = 4 or a=2

The correct answer is (B).

ankurmit wrote:thanks Rahul..nice explanation..I am not able to draw its figure. Can you please help me

Here's the figure, it shows the base of cylindrical tank. Hope this helps.

ankurmit wrote:Nice figure

Thanks again

welcome