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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

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!