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Cricles

by kaf » Thu Apr 02, 2009 2:34 pm
Solution and explanation please

Increasing a circle's radius by 20%, causes the circle's area to increase by how much?

A.100%
B.60%
C.44%
D.40%
E. 25%

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by truplayer256 » Thu Apr 02, 2009 2:38 pm
A=pi*radius squared
If the originial radius equals r, then the area of the circle would be pi*r^2.
Now, if we increased the radius by 20%, the area of the new circle would be pi*(6r/5)^(2)=1.44*pi*r^2. If we compare the area of the circle with radius r to the area of the circle with radius 1.2r, we can clearly see that that area of the circle with radius 1.2r is 44% greater than the area of the circle with radius r.

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by franciskyle » Thu Apr 02, 2009 3:56 pm
A1: (Pi)*(r^2)

A2: (Pi)*(1.2*r)^2 = (Pi)*(1.44)^2

Using the formula:

(X2 - X1) / X1 * 100%

The Pi's & r^2 cancel so:

= (1.44 - 1) / 1 * 100% = 44%
k. Francis

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by gmat740 » Thu Apr 02, 2009 4:14 pm
R(new) = R + 20% R
where R = original radius
R(new) = 1.2R

And A = pi*R^3

So A(new) = pi*(1.2R)^2

A(new) =1.44 [ pi*R^2]

A(new) = 1.44 A

A(new) increase by =( 1.44-1) *100

= 44% Increase