Question

as shown in the figure a, b, c and d are centres of four congruent circles that diameter is 14 cm if a point from the square ABCD is selected such that it does not lie on the circle then find its probability

Answer 1

Given: A, B, C, and D are the centers of four circles that each have a radius of length one unit. If a point is selected at random from the interior of square ABCD

To find: Probability that the point will be chosen from the shaded region,

In the figure we can see 4 circles of radius 1 unit.



Area of quarter circle with centre A:



Since all the circles are of the same radius hence the area of quarter with centre B, C, D will be same as the area of circle of quarter of circle with centre A.

Hence total area covered by 4 quarter circle will be



Side of the square will be 2 units

Area of square ABCD=4 unit2

Area of the shaded portion 

We know that PROBABILITY



Hence probability of the shaded region is 1-puy/4

Answer 2

Radius of circle = 1cm Length of side of square = 1 + 1 = 2cm Area of square = 2 × 2 = 4cm2 Area of shaded region = area of square – 4 × area of quadrant = 4 – 4(1/4)π(1)2 = (4 − π) cm2 Probability that the point will be chosen from the shaded region = (Area of shaded region)/(Area of square ABCD) = (4 - π)/4 = 1 - π-below-fig-points-and-are-the-centers-four-circles-that-each-have-radius-of-length-one-unit