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A circle is inscribed in a square with the diagonal of 4 centimeters. What is the approximate area of the square that is not occupied by the circle? A. 1.7 B. 2.7 C. 3.4 D. 5.4 E. 8
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16 Sep 2014, 00:34
Official Solution:A circle is inscribed in a square with the diagonal of 4 centimeters. What is the approximate area of the square that is not occupied by the circle? A. 1.7 B. 2.7 C. 3.4 D. 5.4 E. 8 The area of a square equals to \(\frac{\text{diagonal}^2}{2}=\frac{4^2}{2}=8\); Next, since the diagonal of the square equals to 4 centimeters then the side of the square equals to \(2\sqrt{2}\) (you can find it for example using Pythagorean theorem: \(a^2+a^2=4^2\)); Now, the radius of inscribed circle will be half of the side of the square, so \(\sqrt{2}\), which makes its area equal to \(\pi{r^2}=2\pi\); Hence, the approximate area of the square that is not occupied by the circle is \(8 2\pi \approx 86.28 = 1.72\). Answer: A
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Re: M0705
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16 Jul 2016, 15:29
Hello,
if the diagonal is of the square is 4, should the side not be 4/2sqrt? Not 2/2sqrt. This is based on the 454590 special triangle rule.
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17 Jul 2016, 00:12
abhilash53 wrote: Hello,
if the diagonal is of the square is 4, should the side not be 4/2sqrt? Not 2/2sqrt. This is based on the 454590 special triangle rule.
Thanks Solve for x: x^2 + x^2 = 4^2.
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Bunuel wrote: A circle is inscribed in a square with the diagonal of 4 centimeters. What is the approximate area of the square that is not occupied by the circle?
A. 1.7 B. 2.7 C. 3.4 D. 5.4 E. 8 Side of the square =4/\(\sqrt{2}\) So area of the square =\((\frac{4}{\sqrt{2}})^2\)=8 and area of the circle=\(\pi\)*\((\frac{4}{(\sqrt{2}*2)})^2\)=4\(\pi\) So the approximate area of the square that is not occupied by the circle=84\(\pi\)=84*(>1.5)=8(>6) Only answer Choice A meets the substruction requirement to be less than 2,which is 1.7 Correct answer A
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Re M0705
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05 Jun 2017, 17:04
I don't agree with the explanation. Answer is wrong here.
it should be 4*pie  8, which is around 4.56.



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06 Jun 2017, 09:37
MountainGMAT wrote: I don't agree with the explanation. Answer is wrong here.
it should be 4*pie  8, which is around 4.56. My friend, the answer is correct here. Please provide your detailed solution and I'll try to find an error you are making there.
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Re: M0705
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08 Jun 2017, 22:52
MountainGMAT wrote: I don't agree with the explanation. Answer is wrong here.
it should be 4*pie  8, which is around 4.56. Hi! 1. The question says circle is inscribed in a square, and not the other way round! and, 2. No way it can be 4*pie. Area of circle will be 2*pie Answer is correct!



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Re: M0705
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06 Dec 2017, 22:43
Hello,
Why wouldn't the circumference of the cirlce be the same as the diagonal of the square? Thus, the radios would be half of the diagonal, or 4...



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06 Dec 2017, 22:54
DouglassJensen wrote: Hello,
Why wouldn't the circumference of the cirlce be the same as the diagonal of the square? Thus, the radios would be half of the diagonal, or 4... Attachment: circleinsquare.png The circumference of a circle is the distance around it. The diagonal or a square is the distance between two opposite vertices. How are those two equal???
>> !!!
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07 Dec 2017, 10:10
Oh my gosh. Clearly, the end of a long day and got mixed up. What I meant was Diameter, not circumference.
Wouldnt the Diagonal of the square equal the diameter of the circle? So then the radius would be 4?



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07 Dec 2017, 10:13
DouglassJensen wrote: Oh my gosh. Clearly, the end of a long day and got mixed up. What I meant was Diameter, not circumference.
Wouldnt the Diagonal of the square equal the diameter of the circle? So then the radius would be 4? Please check the image above. The side of the square = the diameter of the circle.
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Re: M0705
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27 Mar 2018, 21:40
Bunuel wrote: Official Solution:
A circle is inscribed in a square with the diagonal of 4 centimeters. What is the approximate area of the square that is not occupied by the circle?
A. 1.7 B. 2.7 C. 3.4 D. 5.4 E. 8
The area of a square equals to \(\frac{\text{diagonal}^2}{2}=\frac{4^2}{2}=8\); Next, since the diagonal of the square equals to 4 centimeters then the side of the square equals to \(2\sqrt{2}\) (you can find it for example using Pythagorean theorem: \(a^2+a^2=4^2\)); Now, the radius of inscribed circle will be half of the side of the square, so \(\sqrt{2}\), which makes its area equal to \(\pi{r^2}=2\pi\); Hence, the approximate area of the square that is not occupied by the circle is \(8 2\pi \approx 86.28 = 1.72\).
Answer: A Bunuel please explain this part "Next, since the diagonal of the square equals to 4 centimeters then the side of the square equals to \(2\sqrt{2}\) (you can find it for example using Pythagorean theorem: \(a^2+a^2=4^2\));"



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28 Mar 2018, 02:44
sadikabid27 wrote: Bunuel wrote: Official Solution:
A circle is inscribed in a square with the diagonal of 4 centimeters. What is the approximate area of the square that is not occupied by the circle?
A. 1.7 B. 2.7 C. 3.4 D. 5.4 E. 8
The area of a square equals to \(\frac{\text{diagonal}^2}{2}=\frac{4^2}{2}=8\); Next, since the diagonal of the square equals to 4 centimeters then the side of the square equals to \(2\sqrt{2}\) (you can find it for example using Pythagorean theorem: \(a^2+a^2=4^2\)); Now, the radius of inscribed circle will be half of the side of the square, so \(\sqrt{2}\), which makes its area equal to \(\pi{r^2}=2\pi\); Hence, the approximate area of the square that is not occupied by the circle is \(8 2\pi \approx 86.28 = 1.72\).
Answer: A Bunuel please explain this part "Next, since the diagonal of the square equals to 4 centimeters then the side of the square equals to \(2\sqrt{2}\) (you can find it for example using Pythagorean theorem: \(a^2+a^2=4^2\));" \(side^2 + side^2 = 4^2\); \(2*side^2=16\); \(side^2=8\); \(side=\sqrt{8}=2\sqrt{2}\).
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