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How do you find the radius of a circle when you know the area?

The question is: The area of a circle is proportional to the square of the radius. If the area is 113 cm^2 when the radius is 6 cm, find:
the radius of a circle with area 29 cm^2

Please show the working.. It will help me to understand it. Thanks.

A = pi r^2 = 29
r^2 = 29/pi = 9.23
r = 3.04 cm

This entry was posted on Tuesday, May 11th, 2010 at 2:04 am and is filed under circle area. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

7 Responses to “How do you find the radius of a circle when you know the area?”

  1. the area of a circle will always be equal to pi*r^2. Therefore:
    29^2=pi*r^2
    (29^2)/pi=r^2
    From there you can calculate the rest with basic algebra, which i hope you know.
    References :

  2. A = pi r^2 = 29
    r^2 = 29/pi = 9.23
    r = 3.04 cm
    References :

  3. Part (i)

    π r ² = 113

    r ² = 113 / π

    r = [ 113/π ]^(1/2)

    r = 6 cm

    Part (ii)

    r = [ 29/π ]^(1/2)

    r = 3.04 cm
    References :

  4. well A=pi*r^2

    (pi r squared)

    so flip it around

    a/pi = r^2

    so, the square root of a/pi is the radius
    References :
    worked it out

  5. The area is proportional to the square of the radius, so
    r^2 / 36 = 29 / 113 which leads to r = 3.0 cm
    With questions like this, you should look at the number of significant figures. 6 cm is only one significant figure, so strictly the answer should be 3 cm.
    References :

  6. formula for Area of circle = pi x r² (pi has value 3.1415….)

    since we are given area we can rearrange to find r
    r²= A / pi
    r= ±√(A/pi)

    lets plug in A=29 cm²
    r= ±√(29/pi)
    r= ±3.03825….cm
    Note: whenever you square root a value, you must consider its negative value
    eg. (-3)² = 3² = 9

    however in this case the r>0 as length cannot be -ve

    hence r= 3 cm (to one significant figure)

    Hope this helps =D
    References :

  7. Area of Circle = (pi)r^2 , where value of pi = 3.14

    You can directly find the radius by applying above formula

    29(Area of Circle) = 3.14 (value of Pi) * r^2
    hence, r = Sqroot of (29 / 3.14)
    r = 3.03 , which is approximately 3 (your Answer)
    References :

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