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

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Math Expert
Joined: 02 Sep 2009
Posts: 44321
In the figure above, B is the center of the circle with radius 6. What [#permalink]

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16 Nov 2017, 22:55
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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

[Reveal] Spoiler:
Attachment:

2017-11-17_0947_003.png [ 7.93 KiB | Viewed 600 times ]
[Reveal] Spoiler: OA

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GMAT 1: 620 Q46 V29
Re: In the figure above, B is the center of the circle with radius 6. What [#permalink]

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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

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In the figure above, B is the center of the circle with radius 6. What [#permalink]

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17 Nov 2017, 20:42
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KUDOS
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

[Reveal] 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:
$$\frac{s^2}{2}=\frac{6^2}{2}=18$$

(Sector area) - (triangle area)
$$9\pi - 18$$

*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]

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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]

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18 Nov 2017, 02:24

= pi x 6x6 - 1/2x6x6

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]

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20 Nov 2017, 12:28
1
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Expert's post
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

[Reveal] 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.

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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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