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In the figure above, the circle is inscribed in a square that has an a

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In the figure above, the circle is inscribed in a square that has an a  [#permalink]

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New post 11 Oct 2018, 03:01
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In the figure above, the circle is inscribed in a square that has an area of 50. What is the area of the circle?


(A) \(\frac{25\pi}{4}\)

(B) \(\frac{25\pi}{2}\)

(C) \(25\pi\)

(D) \(50\pi\)

(E) \(\frac{625\pi}{16}\)


Attachment:
Capture (3).JPG
Capture (3).JPG [ 12.52 KiB | Viewed 600 times ]

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Re: In the figure above, the circle is inscribed in a square that has an a  [#permalink]

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New post 11 Oct 2018, 03:06
Bunuel wrote:
Image
In the figure above, the circle is inscribed in a square that has an area of 50. What is the area of the circle?


(A) \(\frac{25\pi}{4}\)

(B) \(\frac{25\pi}{2}\)

(C) \(25\pi\)

(D) \(50\pi\)

(E) \(\frac{625\pi}{16}\)


Attachment:
Capture (3).JPG



Area of the square = s^2 = 50 = \(5\sqrt{2}\)

Area of the circle = (\(5\sqrt{2}\)/2)^2 pie = 25 / 2 pie.

The best answer is B.
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Re: In the figure above, the circle is inscribed in a square that has an a  [#permalink]

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New post 11 Oct 2018, 08:52
selim wrote:
Bunuel wrote:
Image
In the figure above, the circle is inscribed in a square that has an area of 50. What is the area of the circle?


(A) \(\frac{25\pi}{4}\)

(B) \(\frac{25\pi}{2}\)

(C) \(25\pi\)

(D) \(50\pi\)

(E) \(\frac{625\pi}{16}\)


Attachment:
Capture (3).JPG



Area of the square = s^2 = 50 = \(5\sqrt{2}\)

Area of the circle = (\(5\sqrt{2}\)/2)^2 pie = 25 / 2 pie.

The best answer is B.


+1 for (B), well explained....
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Re: In the figure above, the circle is inscribed in a square that has an a  [#permalink]

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New post 11 Oct 2018, 09:30
Bunuel wrote:
Image
In the figure above, the circle is inscribed in a square that has an area of 50. What is the area of the circle?


(A) \(\frac{25\pi}{4}\)

(B) \(\frac{25\pi}{2}\)

(C) \(25\pi\)

(D) \(50\pi\)

(E) \(\frac{625\pi}{16}\)


Attachment:
Capture (3).JPG


The Diameter of the circle is the one of the sides of the square.

S^2 (area of the square)= 50 or s=5√2

Area of the circle is πr^2

π* (5√2/2)^2= 25π/2 (B)
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Re: In the figure above, the circle is inscribed in a square that has an a  [#permalink]

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New post 13 Oct 2018, 18:47
Bunuel wrote:
Image
In the figure above, the circle is inscribed in a square that has an area of 50. What is the area of the circle?


(A) \(\frac{25\pi}{4}\)

(B) \(\frac{25\pi}{2}\)

(C) \(25\pi\)

(D) \(50\pi\)

(E) \(\frac{625\pi}{16}\)


Attachment:
Capture (3).JPG


the radius √50/2.

So the area of the circle is:

(√50/2)^2 x π = 50π/4 = 25π/2

Alternate solution:

We can see that area of the inscribed circle is obviously less than the area of the circumscribed square (50) but more than half the area of the square (25). Since we know π is approximately 3.14, of the answer choices, choices C, D and E are too big since each of them is more than 50. Choice A is too small since it’s less than 25. So the correct answer is choice B (and it is between 25 and 50).

Answer: B
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Re: In the figure above, the circle is inscribed in a square that has an a   [#permalink] 13 Oct 2018, 18:47
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