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How to find the radius of a circle if its area is 314 square miles?

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animalover4546 | Student, Undergraduate | Honors

Posted March 6, 2010 at 7:39 AM via web

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How to find the radius of a circle if its area is 314 square miles?

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margaretlouise | Student, Undergraduate | eNotes Newbie

Posted March 6, 2010 at 7:48 AM (Answer #1)

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The formula for the area is A = pi x r^2 (I don't know how to type out mathematic notation!)

So you have to shift the equation around algebraically to find "r"(radius).

First divide both sides by pi; this eliminates pi from the right hand side of the equation and changes the left to A/pi. Now we have:

A/pi [area divided by pi]=r^2 [radius squared]

In order to isolate "r", we need to take the square root of both sides.

So now,

square root of (a/pi) = r

Because you know the area, you can plug it into this equation to solve for r, radius.  Remember the order of operations: divide area by pi FIRST, then take the square root of that number.

If you don't understand one of the steps, I hope you'll let us know.  You need to learn how to do this!  : )

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pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted March 6, 2010 at 7:50 AM (Answer #2)

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To figure this out, you just have to go back to the old formula of area = pi*r^2.  In this equation, r is the radius of the circle.

So, we know the area of the circle so we set up the equation

314 = pi*r^2.

So now we need to divide both sides by pi which is, happily enough, 3.14.  314/3.14 is 100.


So 100 equals r^2.  So to find r (the radius) we take the square root of 100, which is 10.

So the radius of the circle is 10 miles.

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krishna-agrawala | College Teacher | Valedictorian

Posted March 6, 2010 at 11:09 AM (Answer #3)

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The area (A) of a circle having a radius equal to 'r' is given by the formula:

A = (pi)*r^2

Where the Greek letter pi is a constant. This constant is  equal to the length of the circumference of any circle divided by its diameter. Please remember that diameter of a circle is two times its radius. The value of pi rounded off up to fifth decimal place is 3.14159. Value of pi rounded off up to second decimal place is 3.14.

The equation for area of circle can be rearranged as given below to give us the formula for radius of a circle with a given area.

r = [A/(pi)]^1/2

The value of area is given as 314 square miles. Substituting this value of area and value of pi in the above equation for radius we get:

r = (314/3.14)^1/2 = 100^1/2 = 10 miles.

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neela | High School Teacher | Valedictorian

Posted March 6, 2010 at 12:39 PM (Answer #4)

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The area of a circle is pi times radius square,where pi  is constant for all circles.

iI r is the radius of the circle, then the area of the circle  is given by:

pi*r^2 = A..........(1).Since A is given to be 314 square miles, to find r, we make r  the subject in the equation, (1) so that

r = (A/pi)^(1/2) = (314/3.141592654 ) ^(1/2) miles=9.997464892 miles

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princessenotes | Student, Undergraduate | eNoter

Posted March 11, 2010 at 12:28 PM (Answer #5)

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r = (314/3.14)^1/2 = 100^1/2 = 10 miles.

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princessenotes | Student, Undergraduate | eNoter

Posted April 17, 2010 at 10:03 AM (Answer #6)

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To figure this out, you just have to go back to the old formula of area = pi*r^2.  In this equation, r is the radius of the circle.

So, we know the area of the circle so we set up the equation

314 = pi*r^2.

314/3.14 is 100.

10 miles

 

I hoped I helped you! If you need any more help, please email my teacher at helpmathtutor@gmail.com

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nova123 | Student | eNotes Newbie

Posted March 24, 2011 at 2:21 AM (Answer #7)

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A simple formula to solve this problem is: Radius = Area divided by pi squared. Sorry, not squared, find the square root of  the answer, and you should have the radius. So in your case, the answer would be 10 miles, the radius of your circle. I hope this helped!

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laurto | Student, Grade 10 | Valedictorian

Posted December 8, 2013 at 1:38 AM (Answer #8)

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a=pi*r^2

pi=3.14

a=314

314=3.14r^2

divide both sides by pi

100=r^2

find the square root

100=r^2

`sqrt(100)` =`sqrt(r^2)`

10=r

the radius is 10

hope this helped!

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Wiggin42 | Student, Grade 11 | Valedictorian

Posted March 23, 2014 at 4:02 PM (Answer #9)

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A = `pixxr^2`

`r = (A/pi)^(1/2)`

`= (314/pi)^(1/2)`

`= (100)^(1/2)`

`= 10`

``

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acompanioninthetardis | Student, Undergraduate | Valedictorian

Posted May 18, 2014 at 3:12 PM (Answer #10)

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area=pi*r^2. so if your area is 314, and we know that pi is approximately 3.14, you plug those numbers in. giving you

314=3.14*r^2

now we have to isolate the r on one side of the equal sign and move everything else over to the left, to do this we divide by 3.14

314/3.14 = r^2

100= r^2

we then square root both sides. giving us:

10 = r

so the radius is 10.

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atyourservice | Student, Grade 10 | Valedictorian

Posted May 31, 2014 at 2:29 AM (Answer #11)

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to find the answer the first thing you need to know is the formula for the area of a circle which is pi*r^2 and work it backward:

314 square miles

the first thins is to divide 314 by pi which is equal to 3.14 (rounded)

314 / 3.14 = 100

now take care of the r^2 part of the formula by finding the square root of 100

the square root of 100 is 10

the radius is 10

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nisarg | Student, Kindergarten | Valedictorian

Posted June 19, 2014 at 2:48 AM (Answer #12)

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divide 314 by `pi`

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nisarg | Student, Kindergarten | Valedictorian

Posted June 19, 2014 at 2:49 AM (Reply #1)

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then take the square root of the answer and in this case your answer would be 10

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nisarg | Student, Kindergarten | Valedictorian

Posted June 19, 2014 at 2:49 AM (Answer #13)

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divide 314 by  and then take the square root of whats left in this case the answer would be about 10

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ik9744 | TA , Grade 9 | Valedictorian

Posted June 20, 2014 at 1:08 AM (Answer #14)

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Divide 314 square mile by pi

3.14/314 = 10 so your answer is 10.

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