Enclosed by a fence (GMAT Prep)

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alex.gellatly: Master | Next Rank: 500 Posts; Posts: 435; Joined: Wed Nov 16, 2011 7:27 amFollowed by: 16 members; Thanked: 48 times

by alex.gellatly » Mon Jul 02, 2012 9:56 pm

The figure shown (see attachment) represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?

278
341
357
400
441

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Source: Beat The GMAT — Problem Solving | Mon Jul 02, 2012 9:56 pm

theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Mon Jul 02, 2012 10:02 pm

lenght of lines = 2 * 100 = 200

length of arc = 2 x pie * r * 0.25
= 50 * 3.14

evaluate 200 + 50*3.1
evaluate 200 + 50*3.2

The answer should be between these limits

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Jul 02, 2012 10:13 pm

alex.gellatly wrote:The figure shown (see attachment) represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?

The radius of the circle, r = 100 feet
Circumference of the circle = 2Ï€r = 200Ï€ feet

Length of the fence = (2*r + 1/4 of circumference) = (200 + 50Ï€) feet â‰ˆ (200 + 50*3.14) feet = (200 + 157) feet = 357 feet

The correct answer is C.

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didieravoaka: Master | Next Rank: 500 Posts; Posts: 163; Joined: Tue Jan 13, 2015 11:44 am; Thanked: 2 times

by didieravoaka » Tue Jan 26, 2016 9:41 am

Anurag@Gurome wrote:
alex.gellatly wrote:The figure shown (see attachment) represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?
The radius of the circle, r = 100 feet
Circumference of the circle = 2Ï€r = 200Ï€ feet

Length of the fence = (2*r + 1/4 of circumference) = (200 + 50Ï€) feet â‰ˆ (200 + 50*3.14) feet = (200 + 157) feet = 357 feet

The correct answer is C.

I'm a bit confused, could you please break the formula down?
Thanks

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didieravoaka: Master | Next Rank: 500 Posts; Posts: 163; Joined: Tue Jan 13, 2015 11:44 am; Thanked: 2 times

by didieravoaka » Tue Jan 26, 2016 9:48 am

I finally figured it out.
I was trying to apply the formula I know.
Here there are:
length of an arc: x/360 * Circumference
Perimeter of a sector: length of an arc +2r

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