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

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Math Expert
Joined: 02 Sep 2009
Posts: 43789
The diagram shows circular sections of a cone. If x is 20 percent of R [#permalink]

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05 Oct 2017, 05:07
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Difficulty:

35% (medium)

Question Stats:

58% (01:24) correct 43% (00:59) wrong based on 37 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 [ 20.91 KiB | Viewed 540 times ]
[Reveal] Spoiler: OA

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Posts: 783
Location: India
Re: The diagram shows circular sections of a cone. If x is 20 percent of R [#permalink]

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05 Oct 2017, 05:42
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
Manager
Joined: 20 Jan 2016
Posts: 217
Re: The diagram shows circular sections of a cone. If x is 20 percent of R [#permalink]

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06 Oct 2017, 07:12
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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Joined: 22 May 2016
Posts: 1329
The diagram shows circular sections of a cone. If x is 20 percent of R [#permalink]

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06 Oct 2017, 10:54
Bunuel wrote:

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

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

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The diagram shows circular sections of a cone. If x is 20 percent of R   [#permalink] 06 Oct 2017, 10:54
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