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# A circular cloth with a diameter of 20 inches is placed on a

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Intern
Joined: 28 Aug 2013
Posts: 16
A circular cloth with a diameter of 20 inches is placed on a  [#permalink]

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Updated on: 03 Nov 2013, 05:59
2
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:28) correct 21% (01:12) wrong based on 188 sessions

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A circular cloth with a diameter of 20 inches is placed on a circular tray with a diameter of 24 inches. What fraction of the tray's surface is NOT covered by the cloth?

A. 1/6
B. 1/5
C. 11/36
D. 25/36
E. 5/6

I have a silly question but I need some clarification why does it have to be the ratio of the area's and not circumference?

Originally posted by jhonnybravo on 02 Nov 2013, 05:54.
Last edited by Bunuel on 03 Nov 2013, 05:59, edited 2 times in total.
Edited the question and moved to PS forum.
Intern
Joined: 14 Aug 2013
Posts: 34
Location: United States
Concentration: Finance, Strategy
GMAT Date: 10-31-2013
GPA: 3.2
WE: Consulting (Consumer Electronics)
Re: a cetrain cloth with a diameter of 20 inches is placed in a  [#permalink]

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02 Nov 2013, 06:57
1
jhonnybravo wrote:
a certain cloth with a diameter of 20 inches is placed in a circular tray with a diameter of 24 inches . What fraction of trays surface is not covered by a cloth?

1) 1/6
2)1/5
3)11/36
4)25/36
5)5/6

I have a silly question but I need some clarification why does it have to be the ratio of the area's and not circumference?

The questions asks us to find the surface which is not covered by the cloth i.e., area of the surface not covered.
Where as circumference is the length along the edge of the circle,
2*pi*r implies the length of the curve
pi*r^2 implies area enclosed by that curve..hence Area of the circle is considered for this problem

Area of the tray=pi* r^2, where r=12
=>pi*144
Area of the cloth=pi*100
Surface not covered by the cloth=pi*144-pi*100=Pi*44
fraction of trays surface is not covered by a cloth= Pi*44/total area of the tray
=>Pi*44/Pi*144
=>11/36

Hope its clear
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Re: A circular cloth with a diameter of 20 inches is placed on a  [#permalink]

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04 Jul 2017, 15:36
1
jhonnybravo wrote:
A circular cloth with a diameter of 20 inches is placed on a circular tray with a diameter of 24 inches. What fraction of the tray's surface is NOT covered by the cloth?

A. 1/6
B. 1/5
C. 11/36
D. 25/36
E. 5/6

I have a silly question but I need some clarification why does it have to be the ratio of the area's and not circumference?

Let the Radius of Circular tray be = $$R$$

Given diameter of Circular tray = $$24$$ inches

Therefore Radius = $$12$$

Area of Circular tray $$= \pi R^2 => \pi (12^2) => 144\pi$$

Let the Radius of Circular cloth be = $$r$$

Given diameter of Circular cloth = $$20$$ inches

Therefore Radius $$= 10$$

Area of Circular cloth $$= \pi r^2 => \pi (10^2) => 100\pi$$

Area of Tray's surface not covered $$=$$ Area of Circular tray $$-$$ Area of Circular cloth $$=> \pi$$$$R^2 -$$$$\pi$$$$r^2$$

$$144\pi - 100\pi$$ $$=> \pi (144-100)$$ $$=> 44\pi$$

Required fraction = Area of Tray's surface not covered / Total Area of Tray $$=> \frac{44\pi}{144\pi} => \frac{11}{36}$$

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Re: A circular cloth with a diameter of 20 inches is placed on a  [#permalink]

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01 Aug 2018, 16:58
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Re: A circular cloth with a diameter of 20 inches is placed on a &nbs [#permalink] 01 Aug 2018, 16:58
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# A circular cloth with a diameter of 20 inches is placed on a

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