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# In the figure above, a circle is inscribed in a square with an area of

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Math Expert
Joined: 02 Sep 2009
Posts: 53061
In the figure above, a circle is inscribed in a square with an area of  [#permalink]

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17 Jan 2019, 03:32
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Difficulty:

5% (low)

Question Stats:

89% (00:35) correct 11% (00:40) wrong based on 35 sessions

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In the figure above, a circle is inscribed in a square with an area of 16. What is the area of the circle?

A π
B 2π
C 4π
D 8π
E 16π

Attachment:

2019-01-17_1530.png [ 7.04 KiB | Viewed 423 times ]

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Re: In the figure above, a circle is inscribed in a square with an area of  [#permalink]

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17 Jan 2019, 03:47
Bunuel wrote:

In the figure above, a circle is inscribed in a square with an area of 16. What is the area of the circle?

A π
B 2π
C 4π
D 8π
E 16π

Attachment:
2019-01-17_1530.png

Observe that Diameter of circle=Side of the square=$$\sqrt{16}=4$$

Therefore, area of circle=$$π(2)^2=4π$$

Ans. (C)
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Re: In the figure above, a circle is inscribed in a square with an area of  [#permalink]

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17 Jan 2019, 04:16
Bunuel wrote:

In the figure above, a circle is inscribed in a square with an area of 16. What is the area of the circle?

A π
B 2π
C 4π
D 8π
E 16π

Attachment:
2019-01-17_1530.png

Need to look at the figure correctly

Area = 16
side^2 = 16
side = 4

Side of the square can act as the diameter of the circle

Area = π r^2
Area = 4 π

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Re: In the figure above, a circle is inscribed in a square with an area of  [#permalink]

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17 Jan 2019, 05:48

Solution

Given:
• A circle is inscribed in a square
• Area of square = 16

To find:
• The area of the circle

Approach and Working:
Area of square = $$a^2 = 16$$
• Implies, a = 4

And, diameter of the circle = a
• Implies, radius, $$r = \frac{a}{2} = 2$$

Therefore, area of circle = $$ᴨr^2 = 4ᴨ$$

Hence, the correct answer is Option C

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Re: In the figure above, a circle is inscribed in a square with an area of  [#permalink]

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17 Jan 2019, 07:43
Bunuel wrote:

In the figure above, a circle is inscribed in a square with an area of 16. What is the area of the circle?

A π
B 2π
C 4π
D 8π
E 16π

Attachment:
2019-01-17_1530.png

side of square = 4
one of sides of square = diameter of circle
area = 4pi
IMO C
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Re: In the figure above, a circle is inscribed in a square with an area of  [#permalink]

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21 Jan 2019, 18:33
Bunuel wrote:

In the figure above, a circle is inscribed in a square with an area of 16. What is the area of the circle?

A π
B 2π
C 4π
D 8π
E 16π

Attachment:
2019-01-17_1530.png

Since the area of the square is 16, the side of the square = diameter of circle = 4.

So the radius of the circle is 2, and its area is therefore π x 2^2 = 4π.

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Re: In the figure above, a circle is inscribed in a square with an area of   [#permalink] 21 Jan 2019, 18:33
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