SOLUTION: Solve by factoring. The radius of a circle is increased by 3 in., which increases the area by 100 in^2. Find the radius of the original circle. Round to the nearest hundredth. Pl

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve by factoring. The radius of a circle is increased by 3 in., which increases the area by 100 in^2. Find the radius of the original circle. Round to the nearest hundredth. Pl      Log On


   

Question 144072This question is from textbook Beginning Algebra with Applications
: Solve by factoring.
The radius of a circle is increased by 3 in., which increases the area by 100 in^2. Find the radius of the original circle. Round to the nearest hundredth.
Please answer. This question is from textbook Beginning Algebra with Applications

Found 2 solutions by scott8148, edjones:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let r=radius __ (pi)(r^2)+100=(pi)((r+3)^2)

dividing by pi and FOILing __ r^2+(100/pi)=r^2+6r+9 __ subtracting r^2+9 __ (100/pi)-9=6r

dividing by 6 __ (100/(6*pi))-(3/2)=r

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
pi*r^2=A original
pi*(r+3)^2=A+100 new
pi(r^2+6r+9)=A+100
pi(r^2+6r+9)-100=A
pi(r^2+6r+9)-100=pi*r^2
r^2+6r+9-(100/pi)=r^2
6r+9-31.83=0
6r=22.83
r=3.81"
.
Check:
pi*3.81^2=45.49
pi*6.81^2=145.49
.
Ed