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Region Q, shown here, is defined by

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Region Q, shown here, is defined by [#permalink]

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New post 25 Nov 2017, 12:11
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Question Stats:

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Region Q, shown here, is defined by

\((x−6)^{​2} +(y−4)^{2} \leq 100\),

\(y\geq{0}\), and \(x\geq{0}\).

What is the approximate area of Region Q in square units?

A.between 75 and 125
B.between 125 and 175
C.between 175 and 225
D.between 225 and 275
E.between 275 and 325
Attachment:
Capture.PNG
Capture.PNG [ 25.12 KiB | Viewed 803 times ]
[Reveal] Spoiler: OA

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Re: Region Q, shown here, is defined by [#permalink]

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New post 26 Nov 2017, 02:44
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Gnpth wrote:
Region Q, shown here, is defined by

\((x−6)^{​2} +(y−4)^{2} \leq 100\),

\(y\geq{0}\), and \(x\geq{0}\).

What is the approximate area of Region Q in square units?

A.between 75 and 125
B.between 125 and 175
C.between 175 and 225
D.between 225 and 275
E.between 275 and 325
Attachment:
The attachment Capture.PNG is no longer available


Look at the attached figure..
Ans C

Join the parallel lines as shown..
Attachments

IMG_20171126_151118.jpg
IMG_20171126_151118.jpg [ 1.48 MiB | Viewed 740 times ]


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Re: Region Q, shown here, is defined by [#permalink]

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New post 26 Nov 2017, 04:01
Gnpth wrote:
Region Q, shown here, is defined by

\((x−6)^{​2} +(y−4)^{2} \leq 100\),

\(y\geq{0}\), and \(x\geq{0}\).

What is the approximate area of Region Q in square units?

A.between 75 and 125
B.between 125 and 175
C.between 175 and 225
D.between 225 and 275
E.between 275 and 325
Attachment:
The attachment Capture.PNG is no longer available



As we can see the point (6,4) is a centre of the circle. The dash line is a radius wchich is 10. Circle area =\(\pi * r^2\) \(= 100 *\pi\) = 300

The shaded region is around \(\frac{2}{3}\) of the circle area => \(\frac{2}{3} * 300 = 200\)

Hence, the answer is C
Attachments

circle1.jpg
circle1.jpg [ 20.07 KiB | Viewed 719 times ]

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Re: Region Q, shown here, is defined by [#permalink]

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New post 29 Nov 2017, 00:44
Vorovski wrote:
Gnpth wrote:
Region Q, shown here, is defined by

\((x−6)^{​2} +(y−4)^{2} \leq 100\),

\(y\geq{0}\), and \(x\geq{0}\).

What is the approximate area of Region Q in square units?

A.between 75 and 125
B.between 125 and 175
C.between 175 and 225
D.between 225 and 275
E.between 275 and 325
Attachment:
Capture.PNG



As we can see the point (6,4) is a centre of the circle. The dash line is a radius wchich is 10. Circle area =\(\pi * r^2\) \(= 100 *\pi\) = 300

The shaded region is around \(\frac{2}{3}\) of the circle area => \(\frac{2}{3} * 300 = 200\)

Hence, the answer is C


Can you eloborate how you arrived at 2/3??
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Re: Region Q, shown here, is defined by [#permalink]

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New post 29 Nov 2017, 00:45
chetan2u wrote:
Gnpth wrote:
Region Q, shown here, is defined by

\((x−6)^{​2} +(y−4)^{2} \leq 100\),

\(y\geq{0}\), and \(x\geq{0}\).

What is the approximate area of Region Q in square units?

A.between 75 and 125
B.between 125 and 175
C.between 175 and 225
D.between 225 and 275
E.between 275 and 325
Attachment:
Capture.PNG


Look at the attached figure..
Ans C

Join the parallel lines as shown..


Expert can you post a clear cut solution... image is not that clear?
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Re: Region Q, shown here, is defined by [#permalink]

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New post 29 Nov 2017, 01:57
Bhadri1199 wrote:
Vorovski wrote:
Gnpth wrote:
Region Q, shown here, is defined by

\((x−6)^{​2} +(y−4)^{2} \leq 100\),

\(y\geq{0}\), and \(x\geq{0}\).

What is the approximate area of Region Q in square units?

A.between 75 and 125
B.between 125 and 175
C.between 175 and 225
D.between 225 and 275
E.between 275 and 325
Attachment:
Capture.PNG



As we can see the point (6,4) is a centre of the circle. The dash line is a radius wchich is 10. Circle area =\(\pi * r^2\) \(= 100 *\pi\) = 300

The shaded region is around \(\frac{2}{3}\) of the circle area => \(\frac{2}{3} * 300 = 200\)

Hence, the answer is C


Can you eloborate how you arrived at 2/3??


The shaded region is around 70% of the circle and 70% is around 2/3.
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Re: Region Q, shown here, is defined by [#permalink]

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New post 29 Nov 2017, 03:20
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Expert's post
Gnpth wrote:
Region Q, shown here, is defined by

\((x−6)^{​2} +(y−4)^{2} \leq 100\),

\(y\geq{0}\), and \(x\geq{0}\).

What is the approximate area of Region Q in square units?

A.between 75 and 125
B.between 125 and 175
C.between 175 and 225
D.between 225 and 275
E.between 275 and 325
Attachment:
Capture.PNG


The shaded region could be seen as sum of three areas: a quarter of a circle and two rectangles (the shaded region is a bit less)

Area of quarter of a circle \(= (\pi * r^2)/4 = (3.14 * 10^2)/4 = 314/4 = 75\) approx

Area of each rectangle \(= 16*4 + 6*10 = 124\)

So total shaded area will be a bit less than 75 + 124 = 199

The reduced area at the top of the top rectangle is less than 6*2/2 = 6
The reduced area at the right of the lower triangle will be even less.

Answer (C)
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Re: Region Q, shown here, is defined by   [#permalink] 29 Nov 2017, 03:20
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