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16 Sep 2014, 00:34
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A circle is inscribed in a square with a diagonal length of 4 centimeters. What is the approximate area of the square that is not covered by the circle?
A. 1.7
B. 2.7
C. 3.4
D. 5.4
E. 8
A. 1.7
B. 2.7
C. 3.4
D. 5.4
E. 8
16 Sep 2014, 00:34
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Official Solution:
A circle is inscribed in a square with a diagonal length of 4 centimeters. What is the approximate area of the square that is not covered by the circle?
A. 1.7
B. 2.7
C. 3.4
D. 5.4
E. 8
The area of a square can be calculated as \(\frac{\text{diagonal}^2}{2}=\frac{4^2}{2}=8\) square centimeters;
Next, since the area of the square is 8 square centimeters, its side length is \(\sqrt{8}=2\sqrt{2}\) centimeters (because the area of a square is \(side^2\));
The radius of the inscribed circle is half of the side length of the square, which is \(\sqrt{2}\) centimeters. Therefore, the area of the circle is \(\pi{r^2}=2\pi\) square centimeters;
Consequently, the approximate area of the square that is not covered by the circle is \(8- 2\pi \approx 8-6.28 = 1.72\) square centimeters.
Answer: A
A circle is inscribed in a square with a diagonal length of 4 centimeters. What is the approximate area of the square that is not covered by the circle?
A. 1.7
B. 2.7
C. 3.4
D. 5.4
E. 8
The area of a square can be calculated as \(\frac{\text{diagonal}^2}{2}=\frac{4^2}{2}=8\) square centimeters;
Next, since the area of the square is 8 square centimeters, its side length is \(\sqrt{8}=2\sqrt{2}\) centimeters (because the area of a square is \(side^2\));
The radius of the inscribed circle is half of the side length of the square, which is \(\sqrt{2}\) centimeters. Therefore, the area of the circle is \(\pi{r^2}=2\pi\) square centimeters;
Consequently, the approximate area of the square that is not covered by the circle is \(8- 2\pi \approx 8-6.28 = 1.72\) square centimeters.
Answer: A
General Discussion
AbdurRakib
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17 Jul 2016, 06:51
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Bunuel
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
Correct answer A
