The area of a circle is halves when x meters is subtracted from its radius. If the original circle has a radius of 40 m, what is the value of x? Round your answer to the nearest tenth.
Area of original circle = pi * 40^2 = 1600pi m^2
1/2 of this = 800 pi m^2
So
800 pi = pi ( 40 - x)^2
800 = (40 - x)^2 take the positive root
sqrt (800) = 40 - x simplify
20sqrt (2) = 40 - x rearrange as
x = 40 - 20sqrt (2) = 20 [ 2 - sqrt (2) ] m ≈ 11.7 m
