Here is the question:


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 ?

Here is how we solve the problem Goldie:

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.

Take care,
Steve

No no, it makes sense. I just didn't expect to use the percent change formula. Its actually an interesting application. Thanks Steve !