Bunuel wrote:
There are two concentric circles with radii 10 and 8. If the radius of the outer circle is increased by 10% and the radius of the inner circle decreased by 50%, approximately by what percent does the area between the circles grow?
A. 140%
B. 141%
C. 190%
D. 192%
E. 292%
B = big circle, s = small circle
Original:
rB (Big) = 10, Area B = 100
rs (small) = 8, Area s = 64
Area A - Area s = 100-64 = 36
Change:
rB*11/10 = 11
rs*1/2 = 4
New:
Area B = 121
Area s = 16
Area B - Area s = 121 - 16 = 105
Difference in new area / Difference in original area = Percent new over original
105 / 36 = 2 & 33/36 = 2 & 11/12, 1/12 is .083 so it's about 2.92.
We have to remember that "by what percent does the area between the circles grow?" means what is the INCREASE rather than PERCENT OF. So, 2.92 - 1 = 1.92