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A pilot surveys a flat circular area represented by 4π square inches

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A pilot surveys a flat circular area represented by 4π square inches [#permalink]

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16 Nov 2017, 08:27
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Difficulty:

35% (medium)

Question Stats:

63% (00:51) correct 37% (00:32) wrong based on 30 sessions

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A pilot surveys a flat circular area represented by 4π square inches on a map. If 1 inch on the map represents 60 miles, how many square miles does the pilot survey?

(A) 15π
(B) 240π
(C) 900π
(D) 7,200π
(E) 14,400π

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Re: A pilot surveys a flat circular area represented by 4π square inches [#permalink]

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16 Nov 2017, 09:06

We know its a circular area represented by 4pi square inches. Area of a circle is Pi*r^2. So R is = 2 inches.

Given the information we know that 1inch = 60 miles so the area of the circle in terms of miles is ((2*60)^2) * pi.

From there it's just some quick math to get to 14,400 pi.
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Re: A pilot surveys a flat circular area represented by 4π square inches [#permalink]

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16 Nov 2017, 09:29
Bunuel wrote:
A pilot surveys a flat circular area represented by 4π square inches on a map. If 1 inch on the map represents 60 miles, how many square miles does the pilot survey?

(A) 15π
(B) 240π
(C) 900π
(D) 7,200π
(E) 14,400π

$$πr^2 = 4π$$

So, $$r = 2 inch$$

Actual radius on map = 120 miles, so actual area on land is $$120^2π$$ = $$14,400π$$ , Answer will be (E)
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Re: A pilot surveys a flat circular area represented by 4π square inches [#permalink]

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16 Nov 2017, 10:07
Direct calculation
A = 4π sq inch
= 4π * 60 * 60 (since square multiply twice the conversion )
= 14400π

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A pilot surveys a flat circular area represented by 4π square inches [#permalink]

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16 Nov 2017, 11:54
Bunuel wrote:
A pilot surveys a flat circular area represented by 4π square inches on a map. If 1 inch on the map represents 60 miles, how many square miles does the pilot survey?

(A) 15π
(B) 240π
(C) 900π
(D) 7,200π
(E) 14,400π

Map area of circular region in square inches =
$$πr^2=4π$$, $$r^2=4$$, so map $$r=2$$ inches

$$\frac{Map}{Actual}=\frac{1inch}{60mi}=\frac{2in}{120mi}$$
Actual radius of the circular area is 120 miles.

Actual area in square miles =
$$πr^2=(120)^2π=14,400π$$

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Re: A pilot surveys a flat circular area represented by 4π square inches [#permalink]

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17 Nov 2017, 14:27
Bunuel wrote:
A pilot surveys a flat circular area represented by 4π square inches on a map. If 1 inch on the map represents 60 miles, how many square miles does the pilot survey?

(A) 15π
(B) 240π
(C) 900π
(D) 7,200π
(E) 14,400π

Since 1 inch = 60 miles, 1 square inch = 60 x 60 = 3,600 square miles.

Thus, 4π square inches = 4π x 3,600 = 14,400π square miles.

Alternate Solution:

We can create a proportion to solve this question. First, the scale given for the map must be converted to square miles: since 1 inch is 60 miles, 1 square inch = 60 x 60 = 3600 square miles.

The proportion for the number of square miles the pilot surveys is:

1 square inch/3600 square miles = 4π square inches/x

Cross multiplying, we have:

x = 4π x 3600

x = 14,400 π square miles

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Re: A pilot surveys a flat circular area represented by 4π square inches   [#permalink] 17 Nov 2017, 14:27
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