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The circumference of a circle is [#permalink]
15 Sep 2017, 08:42
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The circumference of a circle is \(\frac{ 7}{8}\) the perimeter of a square.
Quantity A 
Quantity B 
The area of the square 
The area of the circle 
A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.
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Last edited by Carcass on 04 Oct 2017, 05:38, edited 2 times in total.
edit the OA




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Re: The circumference of a circle is [#permalink]
16 Sep 2017, 08:01
My solution is: since we now that the circumference of the circle is 7/8 the perimeter of the square, we can set 2*pi*r=7/8*4*l, from which we can derive that r = 7/(4*pi)*l. Then the area of a square is l^2, whereas the area of a circle is pi*r^2, where we can substitute r as above. Then, we have to compare l^2 to 49/(16*pi)*l^2 and since 49/16*pi is less than one, the area of the square is greater. So answer should be A. Why B?



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Re: The circumference of a circle is [#permalink]
16 Sep 2017, 15:45
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IlCreatore wrote: My solution is: since we now that the circumference of the circle is 7/8 the perimeter of the square, we can set 2*pi*r=7/8*4*l, from which we can derive that r = 7/(4*pi)*l. Then the area of a square is l^2, whereas the area of a circle is pi*r^2, where we can substitute r as above. Then, we have to compare l^2 to 49/(16*pi)*l^2 and since 49/16*pi is less than one, the area of the square is greater. So answer should be A. Why B? OE Quote: Because the circumference of a circle depends on π(C = πd), it is best to pick values for the square. If the side of the square is 2, the perimeter is 4(2) = 8 and the area is (2)(2) = 4. Then, circumference of the circle is \(\frac{7}{8} * 8 =7\) Since circumference is 2πr = 7, the radius of the circle is r = 7/2π
Quantity A: The area of the square = 4.
Quantity B: The area of the circle = πr^2 = π (7/2π)^2 = π (7/2π)^2 = π (49/4π^2)= 49/4 π= about 3.9
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Re: The circumference of a circle is [#permalink]
21 Sep 2017, 08:02
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Carcass wrote: IlCreatore wrote: My solution is: since we now that the circumference of the circle is 7/8 the perimeter of the square, we can set 2*pi*r=7/8*4*l, from which we can derive that r = 7/(4*pi)*l. Then the area of a square is l^2, whereas the area of a circle is pi*r^2, where we can substitute r as above. Then, we have to compare l^2 to 49/(16*pi)*l^2 and since 49/16*pi is less than one, the area of the square is greater. So answer should be A. Why B? OE Quote: Because an exterior angle of a triangle is equal to the sum of the two opposite interior angles of the triangle (in this case, the top small triangle), c = a + b. Therefore, d > c and a + b = c taken together imply that d > a + b. Subtract b from both sides: d – b > a. Quantity B is greater. Triangles? Should I divide the square in two triangles? I really don't get how a triangle matters in a comparison between a circle and a square



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Re: The circumference of a circle is [#permalink]
21 Sep 2017, 20:05
IlCreatore wrote: Carcass wrote: IlCreatore wrote: My solution is: since we now that the circumference of the circle is 7/8 the perimeter of the square, we can set 2*pi*r=7/8*4*l, from which we can derive that r = 7/(4*pi)*l. Then the area of a square is l^2, whereas the area of a circle is pi*r^2, where we can substitute r as above. Then, we have to compare l^2 to 49/(16*pi)*l^2 and since 49/16*pi is less than one, the area of the square is greater. So the answer should be A. Why B? OE Quote: Because an exterior angle of a triangle is equal to the sum of the two opposite interior angles of the triangle (in this case, the top small triangle), c = a + b. Therefore, d > c and a + b = c taken together imply that d > a + b. Subtract b from both sides: d – b > a. Quantity B is greater. Triangles? Should I divide the square into two triangles? I really don't get how a triangle matters in a comparison between a circle and a square Sorry for the mismatch. My pdf is so tight that I wrote the explanation of the previous question. Apologize. Fixed both the OA and OE
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Re: The circumference of a circle is
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21 Sep 2017, 20:05





