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

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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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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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Bunuel

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]
Bunuel

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
Shaded region represents 3/4 of the circle....

Thus, area of the shaded region will be $$\frac{3}{4}*π*4^2=12π$$, Answer will clearly be (E) 12π
Re: The circle shown has center O and radius 4. What is the area of the sh [#permalink]
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