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# If a square is inscribed in a circle of radius 4, what is the area of

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Math Expert
Joined: 02 Sep 2009
Posts: 58320
If a square is inscribed in a circle of radius 4, what is the area of  [#permalink]

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29 Jan 2019, 03:43
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25% (medium)

Question Stats:

72% (01:03) correct 28% (00:30) wrong based on 26 sessions

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If a square is inscribed in a circle of radius 4, what is the area of the square?

A. 8
B. 16
C. 32
D. 48
E. 64

M11-32

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Re: If a square is inscribed in a circle of radius 4, what is the area of  [#permalink]

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29 Jan 2019, 03:47
Bunuel wrote:
If a square is inscribed in a circle of radius 4, what is the area of the square?

A. 8
B. 16
C. 32
D. 48
E. 64

M11-32

If square is inscribed in a circle then, Diameter of Circle = Diagonal of the square = a√2 (if a is the side of the square)

i.e. Diameter = 2*4 = a√2

i,e, side of the square, a = 4√2

i.e. Area of the square $$= side^2 = a^2 = (4√2)^2 = 32$$

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Math Expert
Joined: 02 Sep 2009
Posts: 58320
Re: If a square is inscribed in a circle of radius 4, what is the area of  [#permalink]

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29 Jan 2019, 03:49
Bunuel wrote:
If a square is inscribed in a circle of radius 4, what is the area of the square?

A. 8
B. 16
C. 32
D. 48
E. 64

M11-32

The diameter of a circle, which is $$2*4=8$$, is the diagonal of an inscribed square. Area of the square equals to $$\frac{\text{diagonal}^2}{2}=\frac{8^2}{2}=32$$.

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Re: If a square is inscribed in a circle of radius 4, what is the area of  [#permalink]

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29 Jan 2019, 03:51
Bunuel wrote:
If a square is inscribed in a circle of radius 4, what is the area of the square?

A. 8
B. 16
C. 32
D. 48
E. 64

M11-32

diameter of circle would be the diagonal of square = s*sqrt2
8= s sqrt2
s = 4 sqrt2
area of square = 16*2 = 32
IMO C
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Re: If a square is inscribed in a circle of radius 4, what is the area of   [#permalink] 29 Jan 2019, 03:51
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