SOLUTION: The sum of the radii of two circles is 6 cm. If the radius of one of the circles is x cm, form an equation for A, the sum of the areas of the two circles. If the value of A is 2

Question 366921: The sum of the radii of two circles is 6 cm. If the radius of one of the circles is x cm, form an equation for A, the sum of the areas of the two circles.
If the value of A is 20π;, calculate the radius of each circle.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
The sum of the radii of two circles is 6 cm. If the radius of one of the circles is x cm, form an equation for A, the sum of the areas of the two circles.
radius = x
Area = pi*x^2
other radius = 6-x
area = pi*(6-x)^2
..
A= pix^2+pi(6-x)^2
A= pi(x^2+(6-x)^2)
A= pi(x^2+36-12x+x^2)
A=pi(2x^2-12x+36)
A=2pi(x^2-6x+18)
.........
20pi =2pi(x^2-6x+18)
/2pi
10=(x^2-6x+18)
x^2-6x+8=0
(x-4)(x-2)=0
x= 2 OR 4
..
2 & 4 are the radii
...
m.ananth@hotmail.ca

RELATED QUESTIONS
The sum of radii of two circles is 10.5 cm and the difference of their circumferences is... (answered by TimothyLamb)

The sum of diameters of two circles is 112 cm and the sum of their areas is 5236 cm^2.... (answered by TimothyLamb)

Calculate the radius of a circle whose area is equal to the sum of the areas of three?... (answered by rapaljer)

two circles have diameters which differ by 4.00 cm. if the sum of the areas of the... (answered by mananth)

TWO CIRCLES TOUCH EXTERNALLY.THE SUM OF THEIR AREA IS 130 sq cm AND DISTANCE BETWEEN... (answered by solver91311)

How would you solve the following word problem by setting up two equations? The sum of (answered by edjones)

Two circles touch externally.The sum of their areas is 58pi cm^2 and the distance between (answered by lwsshak3)

The diameter of a circle whose area is equal to the sum of the areas of the two circles... (answered by Theo)

The sum of the circumference of two different circles is 40p and the sum of their areas... (answered by josmiceli,MathTherapy)