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

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

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New post 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

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

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New post 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

Answer C

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:

\(πr^2 = (6 km)^2* π = 36π km^2\)

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

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New post 23 Nov 2017, 22:42
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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, \(1 cm^2 = 16 km^2\)

\(Area = 9 π/4 * 16 km^2 = 36π km^2\)

Answer (C)
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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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