Question

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

Answer 1

Answer:

Circle A has a diameter of 38 feet, and Circle B has a diameter of 11 feet.

Step-by-step explanation:

Givens

• The radius of circle A is three feet less than twice the diameter of circle B.

Let's call $r_{A}$ the radius of circle A and $d_{B}$ the diameter of circle B.

The given relation can be modeled as

$r_{A}=2d_{B}-3$

Then, the problem states that the sum of the diameters of both circles is 49 feet, that is

$d_{A}+d_{B}=49$ (1)

And, we know by defintion that $r_{A}=\frac{d_{A} }{2}$, replacing this in the first equation

$r_{A}=2d_{B}-3\\\frac{d_{A} }{2}=2d_{B}-3$ (2)

Now, we have to equations with two unknown variables.

Let's replace the first equation into the second one

$d_{A}+d_{B}=49\\d_{B}=49-d_{A}\\\\\frac{d_{A} }{2}=2d_{B}-3\\\frac{d_{A} }{2}=2(49-d_{A})-3\\d_{A}=4(49-d_{A})-6\\d_{A}=196-4d_{A}-6\\d_{A}+4d_{A}=190\\5d_{A}=190\\d_{A}=\frac{190}{5}=38$

Therefore, the diameter of Circle A is 38 feet.

Let's use this value to find the other diameter

$d_{A}+d_{B}=49\\38+d_{B}=49\\d_{B}=49-38=11$

Therefore, Circle A has a diameter of 38 feet, and Circle B has a diameter of 11 feet.

Answer 2

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)= $(2x-3)$

We know, the diameter of circle is $2r$

Diameter of Circle A is $2\times (2x-3)$

Next as given sum of both circle diameter is 49 feet.

∴ $2(2x-3)+x= 49\ feet$

distributing 2 with 2x and -3

⇒ $4x-6+x= 49$

⇒$5x-6= 49$

Adding both side by 6

⇒$5x=55$

Cross multiplying both side.

⇒$x=\frac{55}{5} = 11$

∴ 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= $(2x-3)$

⇒ Radius of circle A= $(2\times 11-3)= 22-3$

∴ Radius of circle A= 19 feet.

Area of circle= $\pi r^{2}$

Taking π= 3.14

Area of circle A= $3.14\times 19^{2} = 3.14\times 361$

∴ Area of circle A= 1133.54

Circumference of circle= 2πr

Circumference of Circle A= $2\times 3.14\times 19= 119.32$

∴ Circumference of Circle A= 119.32