Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Join the webinar and learn time-management tactics that will guarantee you answer all questions, in all sections, on time. Save your spot today! Nov. 14th at 7 PM PST
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 \(8- 2\pi \approx 8-6.28 = 1.72\).
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=8-4\(\pi\)=8-4*(>1.5)=8-(>6) Only answer Choice A meets the substruction requirement to be less than 2,which is 1.7
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!
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 \(8- 2\pi \approx 8-6.28 = 1.72\).
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: \(a^2+a^2=4^2\));"
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 \(8- 2\pi \approx 8-6.28 = 1.72\).
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: \(a^2+a^2=4^2\));"
close
71% (01:36) correct 
