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The diagram shows circular sections of a cone. If x is 20 percent of R

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The diagram shows circular sections of a cone. If x is 20 percent of R [#permalink]

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New post 05 Oct 2017, 06:07
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

59% (01:24) correct 41% (01:05) wrong based on 31 sessions

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The diagram shows circular sections of a cone. If x is 20 percent of R, by what percentage is the area of circle C greater than the area of circle B? (Note: Figure not drawn to scale)

A. 250%
B. 400%
C. 500%
D. 2400%
E. 2500%

[Reveal] Spoiler:
Attachment:
Cone.png
Cone.png [ 20.91 KiB | Viewed 437 times ]
[Reveal] Spoiler: OA

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Re: The diagram shows circular sections of a cone. If x is 20 percent of R [#permalink]

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New post 05 Oct 2017, 06:42
So basically we have two circles, radius of smaller circle is 20% of radius of larger circle. Let radius of bigger circle = 10, then radius of smaller circle = 2.

Ratio of their areas = pi (10)^2 / pi (2)^2 = 25:1

Since area of bigger circle is 25 times that of smaller circle, it is 2400% more than smaller area. Hence D answer

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Re: The diagram shows circular sections of a cone. If x is 20 percent of R [#permalink]

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New post 06 Oct 2017, 08:12
I will go with E

x=0.2R
Say R=10
therefore, x=2

Area of R= 314
Area of B= 12.56

Increased percentage = (301/12.56). 100
This is approximately equal to 2500%

E

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The diagram shows circular sections of a cone. If x is 20 percent of R [#permalink]

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New post 06 Oct 2017, 11:54
Bunuel wrote:
Image
The diagram shows circular sections of a cone. If x is 20 percent of R, by what percentage is the area of circle C greater than the area of circle B? (Note: Figure not drawn to scale)

A. 250%
B. 400%
C. 500%
D. 2400%
E. 2500%

[Reveal] Spoiler:
Attachment:
Cone.png

The cone does not matter; all we need are areas of two circles.

Choose values

Let R = 5
Let x = 1 (20 percent of 5)

Area of Circle C = \(25\pi\)
Area of Circle B = \(1\pi\)

By what percentage is the area of circle C greater than the area of circle B?

Percent increase = \(\frac{(New - Old)}{Old} * 100\)

\(\frac{(25\pi - 1\pi)}{1\pi} * 100\)

\(\frac{24}{1} * 100\) = 2400 percent

Circle C's area is 2400 percent greater than Circle B's area

ANSWER D

Use multiplier / scale factor
x = .20R

Area of Circle C = \(\pi*R^2\)

Let area of C, \(\pi*R^2 = X\)

Area of Circle B =
(scale factor)\(^2\) * (Area of C)

\((.2)^2(X) =.04X =\)Area of B

Percent increase =

\(\frac{(X) - (.04X)}{(.04X)} * 100\)

\(\frac{.96X}{.04X} = (24 * 100)\) = 2400 percent

Answer D

Kudos [?]: 393 [0], given: 640

The diagram shows circular sections of a cone. If x is 20 percent of R   [#permalink] 06 Oct 2017, 11:54
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