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

Question

https://gmatclub.com/forum/download/file.php?id=42014 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 GAMT_20120410182636313_3890.png

PKN · Accepted Answer

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)

LevanKhukhunashvili · Answer

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

EgmatQuantExpert · Answer

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

ScottTargetTestPrep · Answer

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

Abhishek009 · Answer

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

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

Prep Toolkit

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