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On a map, 1 centimeter represents 4 kilometers. A circle on the map

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Math Expert
Joined: 02 Sep 2009
Posts: 44351
On a map, 1 centimeter represents 4 kilometers. A circle on the map [#permalink]

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23 Nov 2017, 05:41
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On a map, 1 centimeter represents 4 kilometers. A circle on the map with a circumference of 3π centimeters represents a circular region of what area?

(A) 6π km^2
(B) 12π km^2
(C) 36π km^2
(D) 72π km^2
(E) 144π km^2
[Reveal] Spoiler: OA

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Joined: 22 May 2016
Posts: 1426
On a map, 1 centimeter represents 4 kilometers. A circle on the map [#permalink]

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23 Nov 2017, 07:02
Bunuel wrote:
On a map, 1 centimeter represents 4 kilometers. A circle on the map with a circumference of 3π centimeters represents a circular region of what area?

(A) 6π km^2
(B) 12π km^2
(C) 36π km^2
(D) 72π km^2
(E) 144π km^2

Circumference, 2πr, of circle on the map, means radius equals:
$$2πr = 3π$$ cm
$$r = \frac{3}{2}$$ cm

Actual radius of the circular region?

$$\frac{Scale}{Actual} = \frac{1cm}{4km}=\frac{(\frac{3}{2}cm)}{Xkm}$$

$$x = (4) * (\frac{3}{2}cm) = 6 km$$

That is, r = $$\frac{3}{2}$$ cm on the map = actual length of r = $$6$$ km

Actual area of circular region in km, where actual $$r = 6$$ km:

$$πr^2 = (6 km)^2* π = 36π km^2$$

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Re: On a map, 1 centimeter represents 4 kilometers. A circle on the map [#permalink]

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23 Nov 2017, 22:42
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Expert's post
Bunuel wrote:
On a map, 1 centimeter represents 4 kilometers. A circle on the map with a circumference of 3π centimeters represents a circular region of what area?

(A) 6π km^2
(B) 12π km^2
(C) 36π km^2
(D) 72π km^2
(E) 144π km^2

Circumference = 2πr = 3π cm

r = 3/2 cm

$$Area = πr^2 = 9 π/4 cm^2$$

Since 1 cm = 4 km, $$1 cm^2 = 16 km^2$$

$$Area = 9 π/4 * 16 km^2 = 36π km^2$$

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Re: On a map, 1 centimeter represents 4 kilometers. A circle on the map   [#permalink] 23 Nov 2017, 22:42
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On a map, 1 centimeter represents 4 kilometers. A circle on the map

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