##### This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 53
Joined: 09 Feb 2009
Thanked: 1 times

### Cricles

by kaf » Thu Apr 02, 2009 2:34 pm

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%

Master | Next Rank: 500 Posts
Posts: 392
Joined: 15 Jan 2009
Location: New Jersey
Thanked: 76 times
by truplayer256 » Thu Apr 02, 2009 2:38 pm
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.

Senior | Next Rank: 100 Posts
Posts: 32
Joined: 11 Mar 2009
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

MBA Student
Posts: 1194
Joined: 16 Aug 2008
Location: Paris, France
Thanked: 71 times
Followed by:17 members
GMAT Score:710
by gmat740 » Thu Apr 02, 2009 4:14 pm
R(new) = R + 20% R
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

• Page 1 of 1