On a rectangular coordinate plane, a circle centered at (0, 0) is insc

Question

On a rectangular coordinate plane, a circle centered at (0, 0) is inscribed within a square with adjacent vertices at (\(0, −2 \sqrt{2}\)) and (\(2 \sqrt{2}, 0\)). What is the area of the region, rounded to the nearest tenth, that is inside the square but outside the circle?

A. 3

B. 3.2

C. 3.4

D. 3.6

E. 3.8

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A. 3

B. 3.2

C. 3.4

D. 3.6

E. 3.8

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PrashantK0099 · Accepted Answer

Another brillient question by  Bunuel

diagonal of square is = 2√2+2√2= 4√2

Hence side of the sq will be 4 because diag in square is a√2

area of sq = 4 * 4 = 16

just pay attention to circle which is in the square , the diameter of the the circle will be side of sq. i.e = 4

Hence radius will be = 2

area of sq= pi * 2^2 = 3.14 * 4 = 12.56 = 12.6 ( nearest to tenth)

Hence desired area that is inside the square but outside the circle is = area of sq - an area of circle = 16- 12.6 = 3.4

Hence IMO answer will be C = 3.4

Please see the attachment for the diagram for clear understanding.

EgmatQuantExpert · Answer

Given

• On a rectangular coordinate plane, a circle centered at (0, 0) is inscribed within a square with adjacent vertices at (0, 2√2) and (2√2, 0).

To Find

• The area of the region, rounded to the nearest tenth, that is inside the square but outside the circle.

Approach and Working Out

• If you consider the diagram below,
 o The side of the square is the distance between (0, 2√2) and (2√2, 0).
o We can calculate it as 4.
o PQ will be 4 and thus radius will be 2.

• Area of the required region = Area of the square – Area of the circle.
 o Area of the square = 16 square units.
o Area of the circle = π 2^2  = 4π = 4×3.14 = 12.56
o Answer = 16 – 12.56 = 3.44
o ~ 3.4

Correct Answer: Option C

exc4libur · Answer

len_sqr: sqrt = =4
diameter=4, rad=2
area sqr - circle = 4^2 - 2^2*pi,
... 16-4*3.14=16-12-.4-.16=4-.56=3.44
rounded=3.4

Ans (D)

carouselambra · Answer

Most important step is to start with a figure.

Using the formula for diagonal of a square, we get a√2
diagonal of square is = 2√2+2√2= 4√2, hence the side of the square is 4*4 = 16.

Now, the diameter of the circle is nothing but the side of square.
Hence the radius = 2
Area of the circle = 3.14*4

Required answer = 16-(3.14*4) = 3.44 = 3.4

akadiyan · Answer

Required:
Area inside the square but outside the circle

Required Area = Area of square - Area of Circle

Area of Square :
The verticies of square are (0,−2√2) and (2√2,0).
From this we get length of the diagonal is 4√2 and side of square is 4
Area of square is 16

Area of circle :
We know that diameter of the circle is equal to side of square. 
So diameter = 4, Radius = 2

Area of circle = 4π , which then translates to 4*3.14 = 12.56

Area of square - Area of circle = 16-12.56 = 3.44

Ans:   C

hsingh3031 · Answer

Side of Square turns out to be 4

So Diameter of circle is equal to Side of Square = 4

Radius of Circle = 4/2 = 2

Desired Area = Area of Square - Area of Circle

= 4*4 - 3.14 * 2 * 2

= 16- 12.56 = 3.44

Hence C

alwaysHP · Answer

Side of the square =  \sqrt{4*2 + 4*2} = 4

area of square= 16
Now, the diameter of the circle is nothing but the side of square.
Hence the radius = 2
Area of the circle = 3.14*4

portion = 16-(3.14*4) = 3.4

SairamRamo · Answer

Length of the square = distance between (0.-2sqrt2) and (2sqrt2,0) = 4

Distance from the centre of the circle (0,0) to the midpoint of (0.-2sqrt2) and (2sqrt2,0) = circle radius = 2

Area of square - Area of circle = (4*4) - (3.14*2*2) = 4*0.86 = 3.44

IMO C

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On a rectangular coordinate plane, a circle centered at (0, 0) is insc

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GMAT Problem Solving (PS) Questions

On a rectangular coordinate plane, a circle centered at (0, 0) is insc

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