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

Question

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

GMATinsight · Answer

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

Answer: Option C

Bunuel · Answer

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

Answer: C

Archit3110 · Answer

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

Fucio · Answer

The diagonal-side formula didn't come to my mind, so I solved by estimating.

I first calculated the area of a square (that formula I remembered fortunately) as pi*r^2 that in this case would be 3,14*4^2 = 16*3,14 that equals something a slightly bigger then 48.
Since the area of an inscribed square is smaller then the one of the circle the answer must be less then 48; it is definitely not 1/3 of the area of the circle so it must be bigger then 16. The only answer choice that satisfies is 32.

Adit_ · Answer

Do we still get these questions in GMAT Focus or does it again come under the category of common knowledge geometry questions?

Bunuel · Answer

You can ignore this question.

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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