Math
posted by John on .
If the radius of a circle is increased by 1 unit, the area of the circle is increased by 16 pi square units. What is the radius of the original circle?

original radius  r
new radius  r+1
original area = πr^2
new area = π(r+1)^2
π(r+1)^2  πr^2 = 16π
divide by π and expand ...
r^2 + 2r + 1  r^2 = 16
2r = 15
r = 7/5 units
check:
old area = π(7.5)^2 = 56.25π
new area = π(8.5)^2 = 72.25π
difference = 72.25P  56.25π = 16π
all looks good! 
AMAZING. Thanks Much.