Question 1129588
two circles have the same center, but one circle has a radius 6 cm greater than the other.
 The area of the inner circle is 221 cm2 less than the outer circle.
 What is the radius of the smaller circle in centimeters? 
:
let = the radius of the smaller circle
then
(r+6) = the radius of the larger
:
large area - small area = 221 sq?cm
{{{pi*(r+6)^2}}} - {{{pi*r^2}}} = 221
FOIL (r+6)(r+6)
{{{pi*(r^2 + 12r + 36) - pi(r^2) }}} = 221
divide equation by pi
r^2 + 12r + 36 - r^2 = 70.3465
r^2 drops out
12r + 36 = 70.3465
12r = 70.3465 - 36
12r = 34.3465
r = {{{34.3465/12}}}
r = 2.86 cm is the radius of the smaller circle
:
:
:
Check this, find actual area of each (larger radius = 8.86)
{{{pi*8.86^2}}} = 246.61
{{{pi*2.86^2}}} =  25.70
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difference in area: 220.9 ~ 221