SainT Posted September 19, 2007 Report Share Posted September 19, 2007 The question is as follows: If the perimeter of a square and the circumference of a circle are the same, then which one of the two has a smaller area? Explain your answer. I have no clue where to begin, I am incline towards the circle. But Why? Link to comment Share on other sites More sharing options...
foxshox Posted September 19, 2007 Report Share Posted September 19, 2007 Its going to be the circle.. the equation of perimeter for a square is S*4 the equation for a circumference of a circle is pi*d. So to find the area of the square you need to square a side of it. So its S^2. So the side of the square is = to P/4, and when you square it you get P^2/16 as the area. Then we look at the circle. To find the radius of the circle( which you need for the area since A=pi*r^2), we have to divide the circumference by pi and then half that. So the radius is = to P/(2*pi). Then we have to square it and multiply it by pi. So we get (P^2 * pi)/(4*pi^2). We then cancel out to get P^2/(4*pi). So we have to find which one is bigger P^2/16 or P^2/4*pi, and since 1/16 is less then 1/4*pi the circle is bigger. Link to comment Share on other sites More sharing options...
SainT Posted September 20, 2007 Author Report Share Posted September 20, 2007 Its going to be the circle.. the equation of perimeter for a square is S*4 the equation for a circumference of a circle is pi*d. So to find the area of the square you need to square a side of it. So its S^2. So the side of the square is = to P/4, and when you square it you get P^2/16 as the area. Then we look at the circle. To find the radius of the circle( which you need for the area since A=pi*r^2), we have to divide the circumference by pi and then half that. So the radius is = to P/(2*pi). Then we have to square it and multiply it by pi. So we get (P^2 * pi)/(4*pi^2). We then cancel out to get P^2/(4*pi). So we have to find which one is bigger P^2/16 or P^2/4*pi, and since 1/16 is less then 1/4*pi the circle is bigger. I actually worked this out as well my friend but you are dead on, I had a feeling you'd be replyin to this one Link to comment Share on other sites More sharing options...
Jager Posted September 20, 2007 Report Share Posted September 20, 2007 Wow I guess if anyone has any math questions just pm foxshox instead of even posting lol. Closed Link to comment Share on other sites More sharing options...
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