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In the figure above, RSTV is a square inscribed in a circle with radiu

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In the figure above, RSTV is a square inscribed in a circle with radiu  [#permalink]

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New post 14 Nov 2017, 23:41
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In the figure above, RSTV is a square inscribed in a circle with radius r. In terms of r, what is the total area of the shaded regions?

(A) r^2(π – 2)
(B) 2r(2 – π)
(C) π(r^2 – 2)
(D) πr^2– 8r
(E) πr^2 – 4r

Attachment:
2017-11-15_1035_001.png
2017-11-15_1035_001.png [ 7.25 KiB | Viewed 1321 times ]

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Re: In the figure above, RSTV is a square inscribed in a circle with radiu  [#permalink]

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New post 15 Nov 2017, 00:44
Since RSTV is a circle the relationship between r and itrs sides would be 2^1/2 to 1
Area of squre=( 2^1/2*r)^2=2r^2
Area of circle=P*r^2
Area of shaded region=P*r^2 - 2r^2=r^2*(P-2)
Answer A
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Re: In the figure above, RSTV is a square inscribed in a circle with radiu  [#permalink]

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New post 15 Nov 2017, 09:09
Bunuel wrote:
Image
In the figure above, RSTV is a square inscribed in a circle with radius r. In terms of r, what is the total area of the shaded regions?

(A) r^2(π – 2)
(B) 2r(2 – π)
(C) π(r^2 – 2)
(D) πr^2– 8r
(E) πr^2 – 4r

Attachment:
2017-11-15_1035_001.png

Diagonal of the square = \(2r\) , so area of the square = \(4r^2/2\) ir, \(2r^2\)

Area of the circle = \(πr^2\)

So, Area of the shaded region = \(πr^2 - 2r^2\)

Or, Area of the shaded region = \(r^2 ( π- 2 )\) , answer will be (A)
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In the figure above, RSTV is a square inscribed in a circle with radiu  [#permalink]

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New post 16 Nov 2017, 18:36
Bunuel wrote:
Image
In the figure above, RSTV is a square inscribed in a circle with radius r. In terms of r, what is the total area of the shaded regions?

(A) r^2(π – 2)
(B) 2r(2 – π)
(C) π(r^2 – 2)
(D) πr^2– 8r
(E) πr^2 – 4r

Attachment:
2017-11-15_1035_001.png

The total area of the shaded regions equals
(Area of Circle) - (Area of Square)

Area of circle= \(πr^2\)

Area of square
The square's diagonal = 2r

The relationship between a square's diagonal, d, and its side, s, is
\(s^2 = d\), so
\(s = \frac{d}{\sqrt{2}}\)
\(s = \frac{2r}{\sqrt{2}}\)

Area of square =
\(s^2 =\frac{2r}{\sqrt{2}}*
\frac{2r}{\sqrt{2}} =\frac{(4)r^2}{2}= 2r^2\)

Total area of shaded regions
(Circle area) - (square area)
\((πr^2 - 2r^2) =\)
\(r^2(π - 2)\)

Answer A
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Re: In the figure above, RSTV is a square inscribed in a circle with radiu  [#permalink]

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New post 13 Sep 2018, 14:37
Bunuel wrote:
Image
In the figure above, RSTV is a square inscribed in a circle with radius r. In terms of r, what is the total area of the shaded regions?

(A) r^2(π – 2)
(B) 2r(2 – π)
(C) π(r^2 – 2)
(D) πr^2– 8r
(E) πr^2 – 4r

Attachment:
2017-11-15_1035_001.png


A faster approach to get the area of the square, is to treat it as a rombus.
A = (d1 x d2)/2 = 2r x 2r / 2 = 2r^2
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Re: In the figure above, RSTV is a square inscribed in a circle with radiu &nbs [#permalink] 13 Sep 2018, 14:37
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