Area of a circle

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jcnissi: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sat Jun 12, 2010 10:17 pm; Thanked: 1 times

Area of a circle

by jcnissi » Sun Jun 13, 2010 9:35 pm

What is the area of the circular region with center O shown in the figure above? (Please see attachment)

a. 100Ï€
b. 900n
c. 1,600n
d. 2,500n
e. 4,900n

Please note that n is supposed to represent pie. I dont know how to input that symbol on this blog.

Thanks

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Source: Beat The GMAT — Problem Solving | Sun Jun 13, 2010 9:35 pm

albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 am; Location: Bangalore, India; Thanked: 116 times; Followed by:10 members; GMAT Score:770

by albatross86 » Sun Jun 13, 2010 9:53 pm

The distance between the origin (0,0) and the point (30,40) which lies on the circle, represents the radius.

Therefore radius = root [ (40 - 0)^2 + (30 - 0)^2 ] ... formula for the distance between 2 points. This is derived using the Pythagorean Theorem.

Therefore radius = root [ 40^2 + 30^2]
Therefore Area = pi*radius^2
= pi * [40^2 + 30^2]
= pi* [1600 + 900]
= 2500pi

Pick D