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# The circle shown has center O and radius 4. What is the area of the sh

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Math Expert
Joined: 02 Sep 2009
Posts: 56304
The circle shown has center O and radius 4. What is the area of the sh  [#permalink]

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04 Jul 2018, 20:52
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Difficulty:

15% (low)

Question Stats:

78% (00:36) correct 22% (00:42) wrong based on 108 sessions

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The circle shown has center O and radius 4. What is the area of the shaded region?

A. 3π
B. 4π
C. 6π
D. 8π
E. 12π

Attachment:

GAMT_20120410182636313_3890.png [ 7.38 KiB | Viewed 3592 times ]

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Re: The circle shown has center O and radius 4. What is the area of the sh  [#permalink]

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04 Jul 2018, 21:40
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Bunuel wrote:

The circle shown has center O and radius 4. What is the area of the shaded region?

A. 3π
B. 4π
C. 6π
D. 8π
E. 12π

Attachment:
GAMT_20120410182636313_3890.png

Given, the un-shaded sector of the circle makes central angle of $$90^{\circ}$$.
hence, un-shaded region is one-fourth of the total area of the circle & shaded region is three-fourth of the total area of the circle.

Area of shaded region= $$\frac{3}{4}$$($$\pi$$$$r^2$$)=$$\frac{3}{4}$$$$\pi$$*$$4^2$$
=12$$\pi$$
Ans. (E)
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The circle shown has center O and radius 4. What is the area of the sh  [#permalink]

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05 Jul 2018, 01:28
Don't be me, read the stem carefully, thoroughly, attentively, twice.
The shaded region isn't that small region between 3 and 6 o'clock

This question decreased my self-esteem and I fell in deep despair
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Joined: 04 Jan 2015
Posts: 2943
Re: The circle shown has center O and radius 4. What is the area of the sh  [#permalink]

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05 Jul 2018, 04:09

Solution

Given:
• Center of the circle is O
• Radius of the circle is 4

To find:
• The area of the shaded region in the above figure

Approach and Working:
• Area of the circle = $$ᴨr^2$$ (where r is the radius of the circle)

• Area of sector with a central angle of x degrees = $$\frac{x}{360}$$ * area of the circle
o The central angle of the shaded region = 360 – 90 = 270 degrees
o Area of the shaded region = $$\frac{270}{360} * ᴨ * 4^2$$ = 12ᴨ

Therefore, area of the shaded region = 12ᴨ

Hence, the correct answer is option E.

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Re: The circle shown has center O and radius 4. What is the area of the sh  [#permalink]

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09 Jul 2018, 20:00
Bunuel wrote:

The circle shown has center O and radius 4. What is the area of the shaded region?

A. 3π
B. 4π
C. 6π
D. 8π
E. 12π

Attachment:
GAMT_20120410182636313_3890.png

The area of the circle is π x 4^2 = 16π.

Recall that a circle has 360 degrees. The unshaded region is 90/360 = 1/4 of the circle, and so the unshaded region is 3/4 of the circle. Since the shaded region is 3/4 x area of the circle, the shaded region is 3/4 x 16π = 12π.

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Re: The circle shown has center O and radius 4. What is the area of the sh   [#permalink] 09 Jul 2018, 20:00
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