Expert: Sherry Wallin - 3/13/2009

Question
The circumference of a circular plot of land is increased by 10%. What is the best estimate of the total percentage that the area of the plot increased?
(1) 10%
(2) 31%
(3) 21%
(4) 25%
























































Ans:3-21%

Answer
keane~
    I am guessing you would like to know why that is the answer or perhaps you just want it validated?

The relationship between circumference and area is this:
C = pi*d or C = pi*2r since the diameter is two radius's
The area of a circle is of course pi*r^2. The problem tells you that the circumference is increased by 10%.
Essentially by increasing the circumference you have increased the radius/diameter which makes the change in area much more than 10%, because you are squaring the radius when you calculate area. The new circumference is 1.1C = 1.1*pi*2r. The pi and the 2 are constant so you have a radial increase of .1 or 10%. Now put that into the area formula.
The area of the original circle is pi*r^2 and the new circle area is: pi*(1.1r)^2 = pi*1.21r^2, in other words and increase of 21%!