Carcass wrote:
In the figure below, ABCD is a rectangle, and BE and CF are arcs of circles centered at A and D. What is the area of the striped region?
Attachment:
#GREpracticequestion In the figure below, ABCD.jpg
A) \(10 - \pi\)
B) \(2 (5 - \pi)\)
C) \(2 (5 - 2\pi)\)
D) \(6 + 2\pi\)
E) \(5 (2 - \pi)\)
Explanation::The area of the rectangle = 5 * 2 = 10
Now for the arc area;
\(\frac{{Arc Area}}{{Circle Area}} = \frac{90}{360}\)
or Arc area =\(\frac{90}{360} * \pi * {radius}^2\)( radius of the circle = 2)
or Arc area = \(\pi\)
Since there are 2 Arc and both have the same radius ,
Therefore the area covered by the 2 Arc = \(2\pi\)
Therefore the Area of the shaded region = \(10 - 2\pi = 2(5 - \pi)\)
_________________
If you found this post useful, please let me know by pressing the Kudos ButtonRules for PostingGot 20 Kudos? You can get Free GRE Prep Club TestsGRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months
GRE Prep Club tests