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

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Bunuel
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In the figure above, a circle is inscribed in a square with an area of [#permalink] New post   17 Jan 2019, 04:32
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A
B
C
D
E

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83% (00:34) correct 17% (00:37) wrong based on 62 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


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2019-01-17_1530.png
2019-01-17_1530.png [ 7.04 KiB | Viewed 2392 times ]
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C
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Re: In the figure above, a circle is inscribed in a square with an area of [#permalink] New post   17 Jan 2019, 04:47
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


Show Spoiler
Attachment:
2019-01-17_1530.png



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

Hence, radius of circle=2
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] New post   17 Jan 2019, 05:16
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


Show Spoiler
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
radius = 2

Area = π r^2
Area = 4 π

Answer C
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Re: In the figure above, a circle is inscribed in a square with an area of [#permalink] New post   17 Jan 2019, 06:48
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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

Answer: C

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Re: In the figure above, a circle is inscribed in a square with an area of [#permalink] New post   17 Jan 2019, 08:43
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


Show Spoiler
Attachment:
2019-01-17_1530.png



side of square = 4
one of sides of square = diameter of circle
radius = 2
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] New post   21 Jan 2019, 19:33
Expert Reply
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


Show Spoiler
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.

Answer: C
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Re: In the figure above, a circle is inscribed in a square with an area of [#permalink]
21 Jan 2019, 19:33
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