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In the figure above, AB is an arc of a circle with center O. If the le

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Bunuel
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In the figure above, AB is an arc of a circle with center O. If the le [#permalink] New post   10 Jan 2019, 02:21
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In the figure above, AB is an arc of a circle with center O. If the length of arc AB is 5π and the length of CB is 4, what is the sum of the areas of the shaded regions?

A. 25π — 60
B. 25π — 48
C. 25π — 36
D. 100π — 48
E. 100π — 36

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Archit3110
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Re: In the figure above, AB is an arc of a circle with center O. If the le [#permalink] New post   10 Jan 2019, 05:36
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Bunuel wrote:

In the figure above, AB is an arc of a circle with center O. If the length of arc AB is 5π and the length of CB is 4, what is the sum of the areas of the shaded regions?

A. 25π — 60
B. 25π — 48
C. 25π — 36
D. 100π — 48
E. 100π — 36

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Attachment:
2019-01-10_1318.png


from the given info:
2*pi*r *1/4 = 5 *pi
r = 10
for the given figure which is at 90* the point OD = radius = 10 and CD= 8
rectangle has dimension 8 & 6 area = 48

area of the semicircle with radius 10 would be pi * r^2 /4 = pi * 100/4 = 25 pi
area of the shaded part = 25pi-48 ; IMO B
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Re: In the figure above, AB is an arc of a circle with center O. If the le [#permalink] New post   06 Aug 2021, 09:46
Where's the point D here?
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Re: In the figure above, AB is an arc of a circle with center O. If the le [#permalink] New post   06 Aug 2021, 22:32
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sa1112 wrote:
Where's the point D here?


Well D make it as a point on circle for the rectangle such that OD is radius 10 and DC is rectangle length 8
Which we get as sides of triangle ODC 10:8:6

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Re: In the figure above, AB is an arc of a circle with center O. If the le [#permalink] New post   07 Aug 2021, 00:12
Any alternative method to solve this?

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Re: In the figure above, AB is an arc of a circle with center O. If the le [#permalink] New post   09 Aug 2021, 02:28
It took me almost 5mins to solve this sum.. is it really possible to calculate such multi layered sum within 2 minutes.. Question have so many layers like first calculate radius, then area of full circle, area of arc, area of rectangle.
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Re: In the figure above, AB is an arc of a circle with center O. If the le [#permalink]
09 Aug 2021, 02:28
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