The diagram above shows two circular sections of a cone. X is the radius of the smaller circular section, and R is the radius of the larger circular section. If X is 20 percent of R, by what percentage is the area of circle C greater than the area of Circle B?
We can say that the big circle is 25 times the size of the small one. but you mean that the additional surface is 24 because of the 1 initial = -> 1 plus 24 means 25. Right ?
Last edited by Goldie on Mon Jul 13, 2009 11:53 am, edited 1 time in total.
We need to find the areas of both circles. Recall, the area of a circle is equal to (pi)R^2. Since x = 0.2R, the area of the smaller circle, B, is equal to (pi)(0.2R)^2 = 0.04(pi)R^2.
To find the percentage by which the area of the larger circle, C, is greater than the area of the smaller circle, B, we just use the percent change formula. We do this by dividing the difference of the two circular areas by the area of B. So we have: (pi)R^2[1 - 0.04] / 0.04(pi)R^2 = = 0.96 / 0.04 = 24 => 2400% increase
So clearly circle C is 25 times larger than circle B, or 2400% increase. So the right answer is D. I hope this helped you out Goldie. Let me know if further clarification is needed.
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