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

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jhonnybravo
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A circular cloth with a diameter of 20 inches is placed on a [#permalink] New post  Updated on: 03 Nov 2013, 04:59
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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

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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?
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Originally posted by jhonnybravo on 02 Nov 2013, 04:54.
Last edited by Bunuel on 03 Nov 2013, 04:59, edited 2 times in total.
Edited the question and moved to PS forum.
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kusena
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Re: a cetrain cloth with a diameter of 20 inches is placed in a [#permalink] New post  02 Nov 2013, 05:57
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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

Show Spoiler
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] New post  04 Jul 2017, 14:36
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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

Show Spoiler
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 \(=> \frac{44\pi}{144\pi} => \frac{11}{36}\)

Answer (C)...

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Re: A circular cloth with a diameter of 20 inches is placed on a [#permalink] New post  09 Oct 2019, 18:55
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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

Show Spoiler
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 area of the cloth is π x 10^2 = 100π, and the area of the tray is π x 12^2 = 144π. Therefore, 100π/144π = 100/144 = 25/36 of the tray’s surface is covered by the cloth. Thus, 1 - 25/36 = 11/36 of the tray’s surface is NOT covered by the cloth.

Answer: C
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Re: A circular cloth with a diameter of 20 inches is placed on a [#permalink] New post  29 Sep 2021, 21:38
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Radius of the tray =12 units

Area of the tray = pi * 12 *12 =144*pi

Radius of the cloth = 10 inches

Area of the cloth = pi * 10 * 10 =100*pi

Area of the tray's surface that is NOT covered by the cloth = 144*pi - 100*pi

=44*pi

Fraction of the tray's surface that is NOT covered by the cloth = 44*pi/144*pi

=11/36

(option c)

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thesip2323
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Re: A circular cloth with a diameter of 20 inches is placed on a [#permalink] New post  20 Feb 2022, 09:00
I can see I did not do the problem correctly but can someone tell me what my approach was trying to solve vs. what the correct approach was?

pi(12-10)^2 = 4pi which is the area not covered of the tray, so I got 4pi/144pi = 1/36, but I'm not too sure what is different about what I did vs. the approach others took to get 11/36.
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Re: A circular cloth with a diameter of 20 inches is placed on a [#permalink] New post  26 Feb 2022, 09:34
Circular cloth diameter 20 inches
Round tray diameter 24 inches

Circular cloth radius 10 inches
Radius circular tray 12 inches

Circular cloth area 10exp2 x pi

Circular tray area 12exp2 x pi


Fraction of the tray not covered by the cloth:

(12exp2 x pi - 10exp2 x pi)/(12exp2 x pi)

Then:

(144 - 100)144
44/144
22/72
11/36

Answer C
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Re: A circular cloth with a diameter of 20 inches is placed on a [#permalink]
26 Feb 2022, 09:34
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