area of circular region

Since 30,40 are the points on the circle, the distance from the origin to the point on the circle will be the radius.

r^2 = 30^2 + 40^2

r = sqrt 2500

r = 50

area = pi r^2 = 50^2 pi = 2500 pi.

Hence D.

parallel_chase wrote:Since 30,40 are the points on the circle, the distance from the origin to the point on the circle will be the radius.

r^2 = 30^2 + 40^2

r = sqrt 2500

r = 50

area = pi r^2 = 50^2 pi = 2500 pi.

Hence D.

Good solution using the Pythagorean formula.

We can shave some time off if we quickly recognize a 3x:4x:5x triangle in the mix. 3/4/5 is the most commonly tested Pythagorean triplet and almost always shows up in some form on test day.

As soon as you see that you have a 30/40/x right angle triangle, 50 should come to mind as the radius. Then calculate the area as above.

Other important triplets to know:

5x:12x:13x
x:x:xroot2 (right isosceles triangle)
x:xroot3:2x (30/60/90 triangle)

and less tested, but still comes up:

7x:24x:25x

(D)