2014-12-03 09:00:21

A circular disk is placed in front of a light so that it casts a circular shadow on the wall opposite the lamp. If the shadow of the disk is 200% the size of the disk itself, what is the ratio of the radius of the shadow to the radius of the disk?

(A) 1:2
(B) 1:√2
(C) √2:√3
(D) √3: 1
(E) √2: 1

The correct answer is E
Explanation: The area of a circle is πr². Let the radius of the small disk be r, meaning the area of the disk is πr². The shadow is 200% of that, meaning it is 2 times as large. Let the radius of the shadow be R, then the area of it is πR². That is equal to 2πr^2,, meaning

2πr²  = πR². Divide both sides by π to get 2r² = R². Square root both sides to get √2r = R. This means the shadow's radius is the disk's radius times √2, meaning the ratio of the shadow's radius to the disk's is √2:1, making E correct.