Posted by Ramesh Reddy on Sunday, August 21, 2011 at 12:40am.
Call the radii r1 and r2.
The center-to-center distance is
r1 + r2 = 14
The combined area is
130 pi cm^2 = pi(r1^2 + r2^2);
therefore
130 = r1^2 + r2^2
The two equations for r1 and r2 can easily be solved by substitution.
(14 - r2)^2 + r2^2 = 130
196 -28r2 + 2r2^2 = 130
r2^2 -14r2 + 33 = 0
(r2 - 11)(r2 -3) = 0
The radii are 3 and 11 cm
r1= first radius
r2= second radius
r1+r2=14
r2=14-r1
The sum of circles areas is:
r1^2 * ð + r2^2 * ð = 130ð
ð * ( r1^2 + r2^2 ) = 130ð Divide both sides with ð
( r1^2 + r2^2 ) = 130
r1^2 + ( 14 - r1 )^2 = 130
r1^2 + 14^2 - 2 * r1 *14 + r1^2 = 130
r1^2 + 196 - 28 * r1 + r1^2 = 130
2 * r1^2 - 28 * r1 + 196 - 130 = 0
2 * r1^2 - 28 * r1 + 66 = 0 Divide both sides with 2
r1^2 - 14 * r1 + 33 = 0
This equation have 2 solutions:
r1 = 3
and
r1 = 11
When r1 = 3
r2 = 14 - r1 = 14 - 3 = 11
When r1 = 11
r2 = 14 - r1 = 14 - 11 = 3
So radii is :
3 cm and 11 cm
The sum of circles areas:
3^2 * ð + 11^2 * ð =
9 *ð + 121 * ð = 130ð cm^2
P.S.
If you don't know solve equation:
r1^2 - 14 * r1 + 33 = 0
In google type:
Quadratic equation online
When you see list of results click on:
Free Online Quadratic Equation Solver: Solve by Quadratic Formula
When page be open in rectangle type:
r1^2 - 14 * r1 + 33 = 0
and click option solve it!
You will see solution step-by-step.
ð = pi
(14 - r2)^(14 - r2)^2 + r2^2 = 130
what is this ^ symbol represents
please explain.I cant understand it.
madam ......please explain how did u get this step.130 pi cm^2 = pi(r1^2 + r2^2)
how did u get this step.130 pi cm^2 = pi(r1^2 + r2^2)
========================
^ means "to the power"
so
r^2 = radius squared
pi r^2 = pie times radius squared
= area of circle of radius r
similar to drwls ......
radius of smaller -- r
radius of larger --- 14-r
πr^2 + π(14-r)^2 = 130π
r^2 + 196 - 28r + r^2 = 130
2r^2 - 28r + 66 = 0
r^2 - 14r + 33 = 0
(r-3)(r-11) = 0
r = 3 or r = 11
sub back in my definitions.
Radius of 1 circle = x,radius of2 circle=14-x. Now,area of circle = piR2. So,pi(x2)+pi(14-x)2=130pi. Pi(x2+196-28x+x2)=130pi. Pi at both sides is cancelled So 2x2-28x+196-130=0. 2(x2-14x+33)=0. X2-11x-3x+33=0. X(x-11)-3(x-11)=0. So, x= 3,11