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?

Answer 1

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!

Answer 2

AMAZING. Thanks Much.