The radius of Circle A is three feet less than twice the diameter of Circle B. If the sum of the diameters of both circles is 49 feet, find the area and circumference of Circle A

Question

Please help me with this. I don’t understand! Plz give me the answer and equation to work

Answer 1

Hi Bob J.

Given that the Radius of Circle A is 3 less than twice the Diameter of Circle B we

Let D = Diameter of Circle B

Let 2D - 3 = Radius of Circle A

Since the Diameter of a circle is twice the Radius; the Diameter of A by substitution is

2(2D -3) = Diameter of Circle A

Given that the sum of the Diameters is 49, we can solve for D as follows:

D + 2(2D -3) = 49

D + 4D - 6 = 49

5D - 6 = 49

5D = 49 + 6

5D = 55

Divide both sides by 5

D = 55/5 = 11

D = Diameter of Circle B

2D - 3 = Radius of Circle A

(2*11) - 3 = Radius of Circle A

22 - 3 = Radius of Circle A

19 = Radius of Circle A

Diameter of Circle A = 2 * 19 = 38

Circumference of Circle A = πd = 38π =119.38

Area of Circle A = π(Radius)² = (19)²π = 361π = 1134.11

Checking by Substitution

2(2D -3) = 2(2*11 - 3) = 2(22 - 3) = 2(19) = 38 = Diameter of Circle A

Diameter A + Diameter B = 49

38 + 11 = 49

I hope this helps, if you have any questions, send me a message

Answer 2

Let A= radius of circle A

Let B = radius of circle B = half B's diameter. the diameter = 2B

A= 3 less than twice B's diameter = 2(2B)-3 = 4B-3

A= 4B-3 Call this Equation I

49=2A+2B 49 is the sum of the diameters of A and B

A+B =49/2

A=49/2-B call this Equation II

set Equation I = Equation II. They're both = A

4B-3 = 49/2-B Solve for B

5B =49/2+3 = 49/2 + 6/2 (49+6)/2 = 55/2

5B = 55/2 divide by 5

B = 11/2

A= 49/2-11/2 = 38/2 = 19 foot radius for Circle A

General formula for Area is pir^2

General formula for Circumference is 2pir

Area of A = pi(r)^2 = pi(19)^2 = 361pi ft^2 = about 1134 square feet

Circumference of A = 2pir =38pi ft = about 119.4 feet