SOLUTION: The radius of circle B is 2.5 times the radius of circle A. If the area of circle A is 8 square yards what is the area of circle B?

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Question 1115933: The radius of circle B is 2.5 times the radius of circle A. If the area of circle A is 8 square yards what is the area of circle B?
Found 3 solutions by stanbon, josgarithmetic, greenestamps:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The radius of circle B is 2.5 times the radius of circle A. If the area of circle A is 8 square yards what is the area of circle B?
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Area of circle A = pi*r^2 = 8
So radius = sqrt[8/pi]
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Radius of circle B = 2.5*sqrt[8/pi]
Area of circle B = pi[2.5*sqrt[8/pi]]^2= pi[6.25*8/pi] = 6.25*8 = 50 sq yrds
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Cheers,
Stan H.
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Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


You don't need to do any arithmetic using the formula for the area of a circle.

All circles are similar; in similar figures, if the ratio of lengths is a:b, the ratio of areas is a^2:b^2.

The ratio of lengths (radii of the two circles) is given as 2.5:1; so the ratio of areas is (2.5)^2:1^2 = 6.25:1

Then the area of the larger circle is 8*6.25 = 50 square yards.