0

# The sum of the areas of two circles is 130 ft^2.the difference of the areas is 112 ft^2. What the radius of each circle.

I need help with math word problems I am not good with them.i just need help

### 4 Answers by Expert Tutors

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
0
pi r_1^2 + pi r_2^2 = 130 ft^2

pi r_1^2 - pi r_2^2 =112 ft^2

2 pi r_1^2 = 242

pi r_1^2 = 121 => r_1 = sqrt(121/pi) = 11/sqrt(pi) feet, exactly

Using calculator with built-in pi value:
r_1 ≈ 6.20608541902532 feet, approximately

121 + pi r_2^2 = 130

pi r_2^2 = 130 - 121 = 9

r_2 = sqrt(9/pi) = 3/sqrt(pi) feet, exactly

Using calculator with built-in pi value:
r_2 ≈ 1.69256875064327 feet, approximately
Meena S. | Patient & knowledgeable Mathematics & Statistics (SPSS) TutorPatient & knowledgeable Mathematics & St...
4.5 4.5 (57 lesson ratings) (57)
0
Hi Willie,Let radius of ist circle is r1 & radius of 2nd circle is r2.
Area of first circle =  Pie *r1^2
Area of 2nd circle = pie*r2^2
Now sum of areas of two circles=pie(r1^2+r2^2)=130.....Eq-1
Diff of areas=pie(r1^2 -r2^2)=112........Eq-2
adding Eq-1 & Eq-2, We get,2pie*r1^2=242                              ( value of pie = 22/7)

2*22/7*r1^2=242
r1^2=242*7/2*22= 38.5
r1= sq root of 38.5=6.2ft
Now substituting the value of r1^2 inti Eq-1,
pie(r1^2+r2^2)=130
22/7(38.5+r2^2)=130
38.5+r2^2=130*7/22
r2^2=41.36-38.5=2.86
r2= sq root of 2.86=1.7ft
Ans: radius of one circle is 6.2ft & radius 2nd circle is 1.7ft.

Meena from Strongsville,OH

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
0
∏ r1^2 + ∏r2^2 = 130 ft2
∏ r1^2  -  ∏r2^2  = 112 ft^2

r1^2 + r2 ^ 2  = 130 /∏ =41.4
r1^2  - r2 ^ 2  =  112/ ∏=35.7
2 r1^2 = 77.1

r1 ^ 2 = 38.6

r1 = √38.6 = 6.2 ft

r2 ^ 2 = 44.4 - 35.7 = 8.7

r2 = √8.7 = 2.9 ft

Amarjeet K. | Professional Engineer for Math and Science TuroringProfessional Engineer for Math and Scien...
4.6 4.6 (8 lesson ratings) (8)
0
Radius of ince cirlce - R1 and other circle - R2
Area of a circle = pi x R2

As per question

(pi x R12) + ( pi x R22) = 130

(pi x R12) - (pi x R22) = 112

=> R12 + R22 = 130/pi         equation 1
R12 - R22 = 112/pi           equation 2
=>  R12 = 112/pi   + R22  Substitute this value of R12 in equation 1
=> 112/pi  + R22 + R22 = 130/pi
=> 2 R22 = 130/pi - 112/pi = 18/pi
=>  R22 = 18/2pi = 9/pi
=> R2 = √(9/pi) = 3/√pi = 3/1.77 = 1.69 ft

Substitute this value of R2 in equation 2
R12 - 9/pi = 112/pi
R12 = 112/pi + 9/pi = 121/pi
R1 = √(121/pi) = 11/√pi = 6.21 ft