Discussion of Question with ID = 041 under Areas

This is the discussion forum for this question. If you find any mistakes in the solution, or if you have a better solution, then this is the right place to discuss. A healthy discussion helps all of us, so you are requested to be polite and soft, even if you disagree with the views of others. The question and its current solution has also been given on this page.

Advertisement

Question

A gun is fired towards a circular board consisting of two concentric circles of radii 12 and 3 cm. If each bullet is able to hit the board, what is the probability that it will strike the ring, i.e., the area between the inner and outer circles?

A

${15/16}$.

B

${5/7}$.

C

1/2.

D

${15/31}$.

Soln.
Ans: a

The area of the ring is equal to the difference of the areas of the two circles. π($12^2 - 3^2$) = 135π sq. cm. The total area is π × 122 = 144π. The probability of hitting the ring is ${135π}/{144π}$ = ${15/16}$.

Comments and Discussion