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GMAT Prep 1- Land

by nsuen » Sun Jun 12, 2016 9:15 pm
Hi-

In case the picture was not clear: The question is the figure shown 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.
A 278
B 341
C 357
D 400
E 441
The correct answer is C 357

I thought the fence has to cover the land so 1/4 of the area of the land is 250 π, but then it is not in any of the answer, then I re read the question, is said the length of the fence so I start to think about the arc, which I found 50 π, and then it is not in any of the answer choice. It asked for the length, what is it asking for? Thanks in advance.

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by OptimusPrep » Sun Jun 12, 2016 9:25 pm
nsuen wrote:Hi-

In case the picture was not clear: The question is the figure shown 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.
A 278
B 341
C 357
D 400
E 441
The correct answer is C 357

I thought the fence has to cover the land so 1/4 of the area of the land is 250 π, but then it is not in any of the answer, then I re read the question, is said the length of the fence so I start to think about the arc, which I found 50 π, and then it is not in any of the answer choice. It asked for the length, what is it asking for? Thanks in advance.

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Length of the fence means the perimeter of the fence.

Perimeter = 100 + 100 + length of the arc
Length of the arc = 2*Ï€*100 / 4 {Quarter of a circle} = 50Ï€ = 157

Perimeter = 100 + 100 + 157 = 357

Correct Option: C
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by danielle07 » Thu Aug 31, 2017 10:56 pm
How do you get 100 + 100 as the perimeter?
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by [email protected] » Fri Sep 01, 2017 4:59 pm
Hi danielle07,

The perimeter is actually the sum of 3 things: the two radii and the arc (that represents 1/4 of the circumference of the circle).

Circumference of a circle is 2(pi)(radius). We're dealing with 1/4 of the circumference, so we have to multiply that total by 1/4:

(1/4)(2)(pi)(100 feet) = 50pi = about 157 feet

Total perimeter = 100 + 100 + 157 = about 357 feet

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by Jeff@TargetTestPrep » Tue Dec 19, 2017 9:57 am
nsuen wrote:Hi-

In case the picture was not clear: The question is the figure shown 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.
A 278
B 341
C 357
D 400
E 441
Image
We must determine how much fence is needed to enclose the quarter circle.

The curvy part of the fence, which is called an arc, has a length that is equal to ¼ of the circumference of the entire circle.

Since the circle's radius = 100 feet, we can use the following equation:

Circumference = 2Ï€r

Circumference = 2 x π x 100 = 200π

Thus, ¼ of the circumference = ¼ x 200π = 50π

50π ≈ 50 x 3.14 = 157

To enclose the entire quarter circle, we would need approximately 100 + 100 + 157 = 357 feet of fence.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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