Carcass wrote:
Attachment:
GRE The figure above shows a semicircle with center O.jpg
The figure above shows a semicircle with center O and a quarter circle with center R. If OQ = 4 and QR = 6, what is the ratio of the area of the shaded region to the area of the
semicircular region?
(A) 2:3
(B) 4:3
(C) 8:9
(D) 9:4
(E) 9:8
Kudos for the right answer and explanation
Radius of semicircle with center O is 4. The area will be (π4^2)/2 --> 8π.
Radius of quarter-circle with center R is 6. The area will be (π6^2)/4 --> 9π.
Ratio of the shaded region to the area of semicircular region is: 9π:8π --> 9:8.
Therefore the correct answer will be option E.