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dusya [7]
3 years ago
5

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 i

s 49 feet, find the area and circumference of Circle A
Mathematics
2 answers:
BlackZzzverrR [31]3 years ago
7 0

Answer:

<h2>Circle A has a diameter of 38 feet, and Circle B has a diameter of 11 feet.</h2>

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.

yanalaym [24]3 years ago
3 0

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

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