GMAT Prep 1- Land

[nsuen]

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.

[OptimusPrep]

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.

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

[danielle07]

How do you get 100 + 100 as the perimeter?

[[email protected]]

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

GMAT assassins aren't born, they're made,
Rich

[Jeff@TargetTestPrep]

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

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