Each of the small circles in the figure has radius one. The innermost

Question

GMATbuster's Weekly Quant Quiz#8 Ques #5

For Questions from earlier quizzes: Click Here

Each of the small circles in the figure has radius one. The innermost circle is tangent to the six circles that surround it, and each of those circles is tangent to the large circle and to its small-circle neighbors. Find the area of the shaded region.

(A) \(\pi\)

(B) \(1.5\pi\)

(C) \(2\pi\)

(D) \(3\pi\)

(E) \(3.5\pi\)

Show Spoiler

Attachment:

e42bf637d6aea8385012d9ddf6ed3b031156bddb.png [ 10.07 KiB | Viewed 10327 times ]

Show Answer

Official Answer

C

Chethan92 · Answer

The diameter of the larger circle = diameter of 3 smaller circle = 6

Area of the shaded circle = Area of the bigger circle - Area of the 7 smaller circles
9Pi-7Pi
2Pi

C is the answer.

gmatphoru · Answer

Area of large circle = Pi * 3 * 3
Area of all small circles = 7 * Pi * 1 *1

Ar of Large Circle - Total area of all small circles = 2Pi

kavach · Answer

Area of small circle is pi. Total area of 7 Small Circles is 7pi. 
The diametre of big circle is 6. Radius 3. Area 9pi.

The difference is 9pi-7pi = 2pi

nitesh50 · Answer

Each of the small circles in the figure has radius one. The innermost circle is tangent to the six circles that surround it, and each of those circles is tangent to the large circle and to its small-circle neighbors. Find the area of the shaded region.

Area of shaded region= Area of larger- area of 6 smaller

Larger radius= if we join centres of 3 small circles, we get the diameter of the big circle.
Diameter= 2+2+2=6
Radius=3

So Shaded region= 9Pie-6*Pie

=3Pie

Hence Option D answer

saukrit · Answer

Correct answer is C

The outer circle radius is 3pi. Area in 9pi

Inner circle area is pi
for 7 inner circles total area is 7pi

Shaded regio area = 9pi- 7pi= 2 pi .

nkin · Answer

pi*9 - pi*7 = 2*pi

Answer is Option C

gmatphoru · Answer

Answer is C. 2Pi

Posted from my mobile device

sowmiyav · Answer

Diameter of bigger circle = 2+2+2 = 6
Radius of bigger circle = 3
Area of bigger circle = 9 pi
Smaller circle each area =pi
shaded area = bigger area - (7*(smaller area))
 = 9 pi -7 pi =2pi
OPTION C

mishugarg · Answer

number of smaller circles with r=1 ::: 7
area of smaller circles = 7pi

radius of larger circle = radius of smaller circle+diameter of smaller circle= 1+2=3
area of larger circle :: 9pi

Area of shaded region= area of larger circle- area of smaller circles = 9pi-7pi=2pi

Each of the small circles in the figure has radius one. The innermost

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Each of the small circles in the figure has radius one. The innermost

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards