Can someone help me out with this hard math question?
In the figure above, a circle is inside of and outside of a square. if a point is chosen at random from the square abcd, what is the probability that the point is chosen from the shaded region?
Its from Dr Chung’s Tip 9 #3. Ive been stuck trying to understand it for the past 45 minutes.
a) 1/4
b) (pi-50)/(100)
c) (2pi-50)/(100)
d) (PI-2)/(8)
e) (pi-2)/(4)
^ The same problem is #21 on this worksheet
http://www.korpisworld.com/Mathematics/SIT%20for%20SAT/WS%2003%20Skills%206-10.pdf
This is a standard SAT problem (may not be on new SAT) that I teach tutees. You need to find the area circles inscribed in or circumscribed around squares. This is a key SAT type of problem that this problem illustrates.
We need to find the area between the circle and inner square and divide it by the area of the outer square. Let the sides of the outer square be 4, making its area 16. Then the radius of the circle is 2, making its area 4 * pi. The diagonal of the inner square is 4, so its area is 8 by the rhombus area formula; or the sides of the inner square are 2sqrt(2) by the 90-45-45 triangle formula or the Pythagorean Theorem, so the area is (2 sqrt (2))^2 =8. Therefore the area between the circle and inner square is 4* pi - 8. The portion of the total area in the shaded region is (4* pi - 8) /16 = (pi - 2) /4, which is e).
^ Why wouldnt you subtract the larger square from the top?
OOOOOOOOOO OH MY GOODNESS I COMPLETELY UNDERSTAND NOW THANK YOU SOOO MUCH!!!
IM SO STUPID! i kept subtracting the larger square on the top and kept getting wrong answers mean while the whole time i completely forgot that on top we only want the desired area!!!
Thank you so much! i feel so happy now that i understand it!!!