Respuesta :
Answer:
Area of Circle A = 1133.54
Circumference of Circle A= 119.32
Step-by-step explanation:
Given: Sum of both circle diameters= 49 feet.
Circle A radius= Three feet less than twice the diameter of circle B.
Lets assume diameter of Circle B is "x"
∴ Circle A radius (r)= [tex](2x-3)[/tex]
We know, the diameter of circle is [tex]2r[/tex]
Diameter of Circle A is [tex]2\times (2x-3)[/tex]
Next as given sum of both circle diameter is 49 feet.
∴ [tex]2(2x-3)+x= 49\ feet[/tex]
distributing 2 with 2x and -3
⇒ [tex]4x-6+x= 49[/tex]
⇒[tex]5x-6= 49[/tex]
Adding both side by 6
⇒[tex]5x=55[/tex]
Cross multiplying both side.
⇒[tex]x=\frac{55}{5} = 11[/tex]
∴ Diameter of circle B is 11 feet.
Next, subtituting the value of x to get the value of radius for Circle A.
Radius of circle A= [tex](2x-3)[/tex]
⇒ Radius of circle A= [tex](2\times 11-3)= 22-3[/tex]
∴ Radius of circle A= 19 feet.
Area of circle= [tex]\pi r^{2}[/tex]
Taking π= 3.14
Area of circle A= [tex]3.14\times 19^{2} = 3.14\times 361[/tex]
∴ Area of circle A= 1133.54
Circumference of circle= 2πr
Circumference of Circle A= [tex]2\times 3.14\times 19= 119.32[/tex]
∴ Circumference of Circle A= 119.32
The area of circle A is 1,134.57 feet². The circumference of circle A is 119.43 feet.
The diameter of a circle is a straight-line from the center to both ends of the circumference of the circle. A radius is a line from the center of the circle to the circumference of the circle. A radius is half the length of the diameter.
Let:
d = diameter of circle B
r = radius of circle A
r = 2d - 3
Diameter of circle A = 2 x (2d - 3) = 4d - 6
Diameter of circle B can be determined by solving for d:
4d - 6 + d = 49
5d = 55
d = 11
Diameter of circle A = 4(11) - 6 = 38
Radius of circle A = 38/2 = 19 feet
Area of a circle = πr²
22/7 x 19² = 1,134.57 feet²
Circumference of a circle = πD
22/7 X 38 = 119.43feet
To learn more about the area of a circle, please check: https://brainly.com/question/1238286
