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In the figure above, B is the center of the circle with radius 6. What

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Bunuel
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In the figure above, B is the center of the circle with radius 6. What [#permalink] New post   16 Nov 2017, 22:55
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A
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E

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In the figure above, B is the center of the circle with radius 6. What is the area of the shaded region?

(A) 9π
(B) 36 – 9π
(C) 36π – 18
(D) 18 – 9π/2
(E) 9π – 18

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2017-11-17_0947_003.png
2017-11-17_0947_003.png [ 7.93 KiB | Viewed 5734 times ]
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E
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Alexey1989x
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Re: In the figure above, B is the center of the circle with radius 6. What [#permalink] New post   17 Nov 2017, 00:31
Area of shaded region = 1/4 Area of the circle - Area of the triangle ABC = 1/4*P*6^2 - 1/2*6*6=9P-18

Answer E
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In the figure above, B is the center of the circle with radius 6. What [#permalink] New post   17 Nov 2017, 20:42
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Bunuel wrote:

In the figure above, B is the center of the circle with radius 6. What is the area of the shaded region?

(A) 9π
(B) 36 – 9π
(C) 36π – 18
(D) 18 – 9π/2
(E) 9π – 18

Show Spoiler
Attachment:
2017-11-17_0947_003.png

The area of the shaded region =
(Sector area) - (triangle area)

Sector central angle = 90°
Sector = \(\frac{90}{360} =\frac{1}{4}\) circle area

Circle area = \(\pi*r^2 = 36\pi\)
Sector area: \(\frac{36\pi}{4}=9\pi\)

Right isosceles triangle area:
\(\frac{s^2}{2}=\frac{6^2}{2}=18\)

Shaded region's area =
(Sector area) - (triangle area)
\(9\pi - 18\)

Answer E

*OR
Area = \(\frac{b*h}{2}=\frac{6*6}{2}=\frac{36}{2}=18\)
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Re: In the figure above, B is the center of the circle with radius 6. What [#permalink] New post   18 Nov 2017, 02:05
As the angle of the sector is 90 Degrees. We have to find out the Area sector using the formulae 90/360 x π 6^2. Then subtract the area of the Right Angle Triangle.
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Re: In the figure above, B is the center of the circle with radius 6. What [#permalink] New post   18 Nov 2017, 02:24
Area of shaded region

= pi x 6x6 - 1/2x6x6

C should be the answer.

Is my approach correct bunnel ?



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Re: In the figure above, B is the center of the circle with radius 6. What [#permalink] New post   20 Nov 2017, 12:28
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Bunuel wrote:

In the figure above, B is the center of the circle with radius 6. What is the area of the shaded region?

(A) 9π
(B) 36 – 9π
(C) 36π – 18
(D) 18 – 9π/2
(E) 9π – 18

Show Spoiler
Attachment:
2017-11-17_0947_003.png


We see that the area of the shaded region is ¼ of the area of the circle minus the area of triangle ABC.

Since the radius is 6, AB = BC = 6, so we have a 45-45-90 right triangle. So, the area of triangle ABC is 6 x 6 x 1/2 = 18.

The area of the entire circle is 6^2π = 36π. Thus, a quarter of its area is ¼ x 36π = 9π.

Therefore, the area of the shaded region is 9π - 18.

Answer: E
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Re: In the figure above, B is the center of the circle with radius 6. What [#permalink]
20 Nov 2017, 12:28
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