shaded semicircles

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed Mar 04, 2009 4:55 am

In the figure attached, the circle has center Y and the four shaded semicircles each have area 18 pi. What is the circumference of the circle?

(A) 24 pi
(B) 30 pi
(C) 36 pi
(D) 48 pi
(E) 60 pi

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Last edited by sanju09 on Wed Mar 04, 2009 5:08 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Wed Mar 04, 2009 4:55 am

truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Wed Mar 04, 2009 5:01 am

Area of one semi-circle=18pi
pi*r^2/2=18pi
pi*r^2=36pi
r^2=36
r=6
2r=d
The diameter of one semicircle is 12. Since there are 4 semicircles, the diameter of the circle is 12*4=48.
C=Pi*d
C=pi*48=48pi D

Last edited by truplayer256 on Wed Mar 04, 2009 5:14 am, edited 1 time in total.

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed Mar 04, 2009 5:09 am

truplayer256 wrote:Area of one semi-circle=18
pi*r^2/2=18
pi*r^2=36
r^2=36/pi
r=6/sqrt(pi)
2r=d
The diameter of one semicircle is 12/sqrt(pi). Since there are 4 semicircles, the diameter of the circle is 12/sqrt(pi)*4=48/sqrt(pi)
C=Pi*d
C=pi*48/sqrt(pi)=48sqrt(pi).. not an answer choice?

Try again with "the four shaded semicircles each have area 18 pi" now.

The mind is everything. What you think you become. –Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

farooq: Master | Next Rank: 500 Posts; Posts: 140; Joined: Sat Feb 28, 2009 8:51 amFollowed by: 3 members; Location: India; Thanked: 14 times

Re: shaded semicircles

by farooq » Wed Mar 04, 2009 5:15 am

sanju09 wrote:In the figure attached, the circle has center Y and the four shaded semicircles each have area 18 pi. What is the circumference of the circle?

(A) 24 pi
(B) 30 pi
(C) 36 pi
(D) 48 pi
(E) 60 pi

Answer is D.

semi circle area = 18 pi. So the full area will be 36 pi and its radius=6, diameter = 12.

therefore radius of the bigger circle comes 24 and its circum=2*24*pi = 48pi

Regards,
Farooq Farooqui.
London. UK

It is your Attitude, not your Aptitude, that determines your Altitude.

marcusking: Master | Next Rank: 500 Posts; Posts: 106; Joined: Wed Feb 04, 2009 6:09 am; Location: Louisville, KY; Thanked: 8 times

Re: shaded semicircles

by marcusking » Wed Mar 04, 2009 10:05 am

sanju09 wrote:In the figure attached, the circle has center Y and the four shaded semicircles each have area 18 pi. What is the circumference of the circle?

(A) 24 pi
(B) 30 pi
(C) 36 pi
(D) 48 pi
(E) 60 pi

If semi circle is 18pi full circle must be 36pi meaning r of semi circle must be 6 so each semi circles diameter is 12.

There are 4 semi circles that span the diameter of the larger circle
4 * 12 = 48

Circumference = pi(diameter)
Circumference = 48pi
D.

Please start posting the OA

deepoe: Master | Next Rank: 500 Posts; Posts: 151; Joined: Wed Feb 11, 2009 2:45 am; Thanked: 3 times

by deepoe » Wed Mar 04, 2009 10:16 am

The 36PI is the area of one full area or not?

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu Mar 05, 2009 3:43 am

The circumference of the circle is equal to D pi , where D is the diameter of the circle. The diameter of the circle is the sum of the diameters of the four semicircles. The four semicircles have equal area, so they must also have equal radii. Let r be the radius of one of the semicircles. Each of the four semicircles has area 18 pi, so 18 pi = ½ pi r^2. Solving for r gives r = 6. Therefore, the sum of the diameters of the four semicircles is 2 r + 2 r + 2 r + 2 r = 8 r = 48. Thus 48 is also the diameter D of the circle, and the circumference of the circle is [spoiler]D pi = 48 pi[/spoiler], which is choice [spoiler](D)[/spoiler].

The mind is everything. What you think you become. –Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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