The sum of the circumference of two circles is 38π cm and the sum of their areas is 193π cm². Calculate the radii of the circles.
Answers
Answer:
Let r1 be the radius of circle 1 and r2 the radius of circle two. Then the sum of the circumferences is
2pi(r1 + r2)
Since we know this equals 38pi, we have 19 = r1 + r2.
The sum of their areas is
pi( (r1)^2 + (r2)^2)
Since we know this equals 193pi, we have 193 = (r1)^2 + (r2)^2.
We can use substitution to solve the following system of two equations in two unknowns:
19 = r1 + r2
193 = (r1)^2 + (r2)^2
From the first equation, we find r1 = 19 - r2. Substitution into the second equation gives
193 = (19 - r2)^2 + (r2)^2,
or,
0 = (r2)^2 - 19r2 + 84.
Applying the quadratic formula gives
r2 = [19 +/- sqrt(361 - 4(84))] / 2
= [19 +/-5 ] /2
= 12 or 7.
Substitution these two possible solutions for r2 in to r1 = 19 - r2 gives r1 = 7 when r2 is 12 and r1 = 12 when r2 = 7.
That is, the two solutions for the pair (r1,r2) are (12, 7) and (7, 12).
Answer:
R1=12cm
R2=7cm
Hope it will help.you