SOLUTION: If the radius of a circle is increased to 200% of its original size, then the area of the circle is increased to what percentage of its original size? a. 200% b. 400% c. 800% d.

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Question 322351: If the radius of a circle is increased to 200% of its original size, then the area of the circle is increased to what percentage of its original size?
a. 200% b. 400% c. 800% d. 40,000% e. none of these
Answer by J2R2R(94) (Show Source):
You can put this solution on YOUR website!
Area is a square measure and if the radius is increased to 200% (twice) its original size then the area of the circle increases to 400% of its original size (4 times = twice squared).

Area = pi r^2.
Doubling r gives Area = pi (2r)^2 = pi 4 r^2 = 4 pi r^2 showing it is now four times the size it was before.

NB Best be careful how you word this since if something has increased to twice its original size, it has increased its size by 100%. If it had increased its size by 200% it would then be three times its size. When you talk about an increase in size you are referring to how much it has grown or got bigger as a multiple of the original size, not the new size as a multiple of the original size. It is always one multiple bigger than the multiple of the size it has grown since that is what it was before it grew.

The size of the radius has increased by 100% (once) to 200% (twice) its original size and the area of the circle has increased by 300% to 400% of its original size.