« What is the formula for finding the area of a Quadrilateral?
I won a 1000 dollar online shopping spree from mountain area should I do it? »

What is the ratio of the area of the circle to the area of the square in this problem?

From a piece of tin in the shape of a square 6 inches on a side, the largest possible circle is cut out. Of the following, the ratio of the area of the circle to the area of the original square is closest in value to…:

F. 4/5
G. 2/3
H. 3/5
J. 7/9
K. 3/4

Please explain how you found your answer. Thanks.

J. 7/9

The area of the square is one side multiplied by the other side, so it’s 6×6=36.

The area of the circle is pi times the radius squared. The radius is 3, so the radius squared is 9. 9 times pi, which is 3.14 is about 28.26.

To find the ratio of the circle to the square, you do 28/36, which reduces to 7/9.

This entry was posted on Saturday, June 19th, 2010 at 6:38 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.

6 Responses to “What is the ratio of the area of the circle to the area of the square in this problem?”

  1. 9pi/36 = pi/4 which is more closer to 7/9.

    J
    References :

  2. Since the square is 6 inches on a side, that means if you cut it in half it would be 3 inches. that means the largest possible circle would be one centered at the middle of the square and is drawn 3 inches out all the way around. the equation for area of a circle is Pi*r*r (pi times r squared) and the area of a square is just a side of the square, squared (lol) so the area of the square would be 36 and the area of the circle would be about 27, so it would be k, 3/4
    References :

  3. r = 3
    A = Pi (3)^2 = 9 Pi

    SQ: A=6X6=36

    9Pi/36 = Pi/4 =.7854

    3/4 = .75
    7/9 = .777
    4/5 = .8

    So 7/9 is the closest.
    References :

  4. J. 7/9

    The area of the square is one side multiplied by the other side, so it’s 6×6=36.

    The area of the circle is pi times the radius squared. The radius is 3, so the radius squared is 9. 9 times pi, which is 3.14 is about 28.26.

    To find the ratio of the circle to the square, you do 28/36, which reduces to 7/9.
    References :

  5. The area of the sqaure is 6*6 =36

    The area of the circle is π(3*3) (since our circle has diameter 6, and thus radius 3) ~ 28.274

    28.274/36 ~ 0.785

    the decimal values of the fractions are:

    F. 4/5 = 0.8
    G. 2/3 ~ 0.667
    H. 3/5 = 0.6
    J. 7/9 ~ 0.778
    K. 3/4 = 0.75

    Obviously it’s down to J or K. 0.785 – 0.75 = 0.035, while 0.785 – 0.778 = 0.007

    Thus J is the correct answer.
    References :

  6. Hi Kristina, this is the way that I would answer this question:
    The square is 6inches on each side, if you cut out a circle from this square the ends of the largest possible circle would be at the ends of the square, meaning that the diameter of the circle would be 6 inches (thus, the radius of the circle would be 3 inches), now, find the area of each:

    Area of square=length times width=6×6=36 inches squared

    Area of circle=pie times (r^2)=approximately: (3.14)x(3^2)=3.14×9=28.26 inches squared

    Now, find the ratio: (area of circle)/(area of original square)=(28.26 inches squared)/(36 inches squared)=0.785=approximately 7/9, meaning that the answer is J. (7/9=7.777…, which is the closest of the above values to 0.785), I hope that helps :)
    References :
    I took a lot of math courses in high school and am currently taking some university level math

Leave a Reply