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

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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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New post 04 Jul 2018, 20:52
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A
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E

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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
GAMT_20120410182636313_3890.png [ 7.38 KiB | Viewed 795 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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New post 04 Jul 2018, 21:40
Bunuel wrote:
Image
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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New post 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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Re: The circle shown has center O and radius 4. What is the area of the sh  [#permalink]

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New post 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.

Answer: 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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New post 09 Jul 2018, 20:00
Bunuel wrote:
Image
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.

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