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

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
In the figure above, the circle is inscribed in a square that has an a  [#permalink]

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11 Oct 2018, 02:01
00:00

Difficulty:

5% (low)

Question Stats:

97% (01:00) correct 3% (02:01) wrong based on 44 sessions

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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 [ 12.52 KiB | Viewed 489 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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11 Oct 2018, 02:06
Bunuel wrote:

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.

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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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11 Oct 2018, 07:52
selim wrote:
Bunuel wrote:

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.

+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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11 Oct 2018, 08:30
Bunuel wrote:

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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13 Oct 2018, 17:47
Bunuel wrote:

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

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).

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Re: In the figure above, the circle is inscribed in a square that has an a   [#permalink] 13 Oct 2018, 17:47
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