Question

What is the probability that a randomly thrown dart that lands within the rectangle lands within a shaded region? All of the circles are congruent, and the diameter of each circle is 28 cm. A. 0.112 B. 0.196 C. 0.697 D. 0.785

Answer 1

Answer: option D. 0.785

Explanation:

1) the probability will be equal to the area of the shaded region divided by the area of the rectangle:

                      area of the shaded region
probability = -------------------------------------
                        area of the rectangle

2) call r the radius of the circles (all are equal)

area of one circle = π (r^2)

area of the four circles = 4π(r^2) = area of the shaded region

3) area of the rectangle

length of the rectangle: 2r
height of the rectangle: 8r

area of the rectgangle = (2r)(8r) = 16 r^2

4) probability = 4π(r^2) /[(16)(r^2)] = π / 4

use π = 3.1416

probability = 3.1416 / 4 = 0.785

And you do not need to use the diameter given. The answer does not depend on this number.