What is the probability that a point chosen at random in the given figure will be inside the larger circle and outside the smaller circle?
Enter your answer, as a fraction in simplest form, in the box.
P(inside larger circle and outside smaller circle) =
6cm and 14 cm
To find the probability of a point being inside the larger circle and outside the smaller circle, we need to find the area of the shaded region between the two circles and then divide it by the total area of the larger circle.
The area of the larger circle is πr^2 = π(14/2)^2 = 49π cm^2
The area of the smaller circle is πr^2 = π(6/2)^2 = 9π cm^2
The area of the shaded region between the two circles can be found by subtracting the area of the smaller circle from the area of the larger circle:
49π - 9π = 40π cm^2
Therefore, the probability of a point being inside the larger circle and outside the smaller circle is:
P(inside larger circle and outside smaller circle) = (40π cm^2) / (49π cm^2) = 40/49
So, the probability is 40/49.