How to find the radius of a circle if its area is 314 square miles?
14 Answers
pohnpei397 | College Teacher | (Level 3) Distinguished Educator
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.
ik9744 | Student, Grade 9 | (Level 1) Valedictorian
Divide 314 square mile by pi
3.14/314 = 10 so your answer is 10.
nisarg | Student, Grade 11 | (Level 1) Valedictorian
divide 314 by and then take the square root of whats left in this case the answer would be about 10
nisarg | Student, Grade 11 | (Level 1) Valedictorian
divide 314 by `pi`
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nisarg | Student, Grade 11 | (Level 1) Valedictorian
then take the square root of the answer and in this case your answer would be 10
atyourservice | Student, Grade 11 | (Level 3) Valedictorian
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
acompanioninthetardis | Student, Undergraduate | (Level 1) Valedictorian
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.
Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian
A = `pixxr^2`
`r = (A/pi)^(1/2)`
`= (314/pi)^(1/2)`
`= (100)^(1/2)`
`= 10`
``
laurto | Student, Grade 10 | (Level 1) Valedictorian
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!
nova123 | Student | eNotes Newbie
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!
princessenotes | Student, Undergraduate | (Level 1) Honors
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
princessenotes | Student, Undergraduate | (Level 1) Honors
r = (314/3.14)^1/2 = 100^1/2 = 10 miles.
neela | High School Teacher | (Level 3) Valedictorian
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
krishna-agrawala | College Teacher | (Level 3) Valedictorian
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.
margaretlouise | Student, Undergraduate | (Level 1) eNoter
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! : )