In the figure above, the points A,B,C,D and E lie on the a line. A is on both circles, B is the centre of the smaller circle, C is the centre of the larger circle, D is on the smaller circle and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?
(I) AB=3 and BC=2
(2)CD=1 and DE=4
To find the area of a circle the radius of the circle is required. The area of the circle = (pi)*radius*radius.
AB = is the radius of the inner circle
AC = is the radius of the inner circle
The required area= (area of the outer circle)-(area of the inner circle)
Lets take statement (I)
AB= 3 and BC =2. The area of the outer circle can be computed as the radius of the outer circle is AC(AB+BC).The radius of the inner circle is AB. The difference in the two areas will give the numerical answer.
It is not necessary to calculate the exact numerical value. It is just enough to know that the answer can be determined with the data given. Time can be saved.
Statement(I) alone is sufficient.
Let’s take statement (II)
CD+DE=CE=CA which is the diameter of the bigger circle.
The diameter of the smaller circle is CA+CD. The radius of the smaller circle is half the diameter. Hence the radius and the diameter of the inner circle can be computed. As the radii of the bigger and inner circle are computed, the required area can be determined.
Statement (II) alone is sufficient.
Hence answer is D.
Questions such as “what is the value of ...?” , “determine the value of ...?“ can be attacked in this manner.