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A circle of radius 4 cm is carved with a sharp knife into Updated on: 16 Jul 2006, 13:03
Originally posted by kevincan on 15 Jul 2006, 08:00.
Last edited by kevincan on 16 Jul 2006, 13:03, edited 3 times in total.
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A circle of radius 4 cm is carved with a sharp knife into the middle of a square board that has a perimeter of 100cm. The portion of the board that is within 2 cm of either the edge of the board or the carved path of the circle is painted black. What percent of the entire board is painted black?

(A) 39.5% (B) 41.5% (C) 43.5% (D) 45.5% (E) 47.5%



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A circle of radius 4 cm is carved with a sharp knife into 15 Jul 2006, 10:00
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Hey...How can a square have a diameter of 100 cm..., DId i read it wrong...or I guess it;s a typo..

Cud u please clarify tht..
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A circle of radius 4 cm is carved with a sharp knife into 15 Jul 2006, 16:39
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I am getting 43.5%, when we assume that the edge of circle and edge of square are atleast 4cm apart.

But if circle is carved on edge then the black painted area will be less and if carved on a corner then black painted area will be even least.

I think this is an ambiguous question.
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A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 00:15
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Good work- the question has been corrected- the original version I came up with had concentric circles and thus avoided this possibility. Thanks!
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A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 02:56
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ps_dahiya
I am getting 43.5%, when we assume that the edge of circle and edge of square are atleast 4cm apart.

But if circle is carved on edge then the black painted area will be less and if carved on a corner then black painted area will be even least.

I think this is an ambiguous question.
Show more



Hey Dahiya, wen it says, the painted area has to 2 b 2 cms from both edge of circle n edge of board, u have to subtract the area of a circle of radius 6 cms (2+ 4 cms radius) from the area of a square with side 21cms(25 cms is the boards side, cut 2 cms frm each side), the remainin part is the painted area..

Hope the explanation makes sense..plz..point out any loopholes
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A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 07:10
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kevincan
Not all the circle is painted black!
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In my explanation, I subtract the area of the ciricle with radius 6, so im not paintin any part of the circle..does it make sense...
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Raghavender
kevincan
Not all the circle is painted black!

In my explanation, I subtract the area of the ciricle with radius 6, so im not paintin any part of the circle..does it make sense...
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But some of the circle is painted back
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A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 07:28
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kevincan
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Not all the circle is painted black!

In my explanation, I subtract the area of the ciricle with radius 6, so im not paintin any part of the circle..does it make sense...

But some of the circle is painted back
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Hey mayb I missd something, but I cant c anywhere, where he implies that the circle is painted black...cud u plzz...help me out...

I read it like this...there is a square board, in which a circle is cut out. then in the remainin part of the board,(square with a hole) he paints some part...
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A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 10:32
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The portion of the board that is within 2 cm of either the edge of the board or the circle is painted black
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A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 12:38
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kevincan
A circle of radius 4 cm is carved with a sharp knife into the middle of a square board that has a perimeter of 100cm. The portion of the board that is within 2 cm of either the edge of the board or the circle is painted black. What percent of the entire board is painted black?

(A) 39.5% (B) 41.5% (C) 43.5% (D) 45.5% (E) 47.5%
Show more



(20pi +184)/(625-16pi)

but the problem is how to approximate to arrive at the answer. % are too close .......

in the exam i would pick 43.5 and move on
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A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 21:39
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Hey old dream,

cud u plzz give ur explanation for ur sol:(20pi +184)/(625-16pi)
I did not get it clearly
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A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 22:00
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old_dream_1976
kevincan
A circle of radius 4 cm is carved with a sharp knife into the middle of a square board that has a perimeter of 100cm. The portion of the board that is within 2 cm of either the edge of the board or the circle is painted black. What percent of the entire board is painted black?

(A) 39.5% (B) 41.5% (C) 43.5% (D) 45.5% (E) 47.5%


(20pi +184)/(625-16pi)

but the problem is how to approximate to arrive at the answer. % are too close .......

in the exam i would pick 43.5 and move on
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When they say entire board, should we consider the original board i.e. area = 625 sq cm? So should we subtract 16Π from the denominator?
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A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 22:11
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Length of each side of the square = 100/4 = 25cm

The sum of the difference between the square of sides 25cm and 21 cm, and the difference between a circle of 12cm diameter and 8cm diameter will be the total area painted.

Painted area
= (25^2 - 21^2) + [(pi*6^2) - (pi*4^2)]
= 184 + 20pi

Percentage = (184 + 20pi)/25^2 * 100 = 39.5%
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A circle of radius 4 cm is carved with a sharp knife into 17 Jul 2006, 19:43
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yup yup..ywilfred, now understood the solution..thanx
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A circle of radius 4 cm is carved with a sharp knife into 17 Jul 2006, 21:30
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ywilfred
Length of each side of the square = 100/4 = 25cm

The sum of the difference between the square of sides 25cm and 21 cm, and the difference between a circle of 12cm diameter and 8cm diameter will be the total area painted.

Painted area
= (25^2 - 21^2) + [(pi*6^2) - (pi*4^2)]
= 184 + 20pi

Percentage = (184 + 20pi)/25^2 * 100 = 39.5%
Show more

ywilfred,

the question says "within" 2 cm of the carved path of the circle but you assumed outside the edge of the carved path.

shouldn't the Percentage be = (25^2 - 21^2) + [(pi*4^2) - (pi*2^2)] =
(184 + 12pi)/25^2 * 100

kevincan
A circle of radius 4 cm is carved with a sharp knife into the middle of a square board that has a perimeter of 100cm. The portion of the board that is within 2 cm of either the edge of the board or the carved path of the circle is painted black. What percent of the entire board is painted black?

(A) 39.5% (B) 41.5% (C) 43.5% (D) 45.5% (E) 47.5%
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A circle of radius 4 cm is carved with a sharp knife into 17 Jul 2006, 21:53
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ywilfred
Length of each side of the square = 100/4 = 25cm

The sum of the difference between the square of sides 25cm and 21 cm, and the difference between a circle of 12cm diameter and 8cm diameter will be the total area painted.

Painted area
= (25^2 - 21^2) + [(pi*6^2) - (pi*4^2)]
= 184 + 20pi

Percentage = (184 + 20pi)/25^2 * 100 = 39.5%

ywilfred,

the question says "within" 2 cm of the carved path of the circle but you assumed outside the edge of the carved path.

shouldn't the Percentage be = (25^2 - 21^2) + [(pi*4^2) - (pi*2^2)] =
(184 + 12pi)/25^2 * 100

kevincan
A circle of radius 4 cm is carved with a sharp knife into the middle of a square board that has a perimeter of 100cm. The portion of the board that is within 2 cm of either the edge of the board or the carved path of the circle is painted black. What percent of the entire board is painted black?

(A) 39.5% (B) 41.5% (C) 43.5% (D) 45.5% (E) 47.5%
Show more


Hmm.... good point.. I took the meaning 'within 2cm' to be anywhere 2cm outside of the circle or inside the board.... but I think you can take it the other way round and say 2cm inside the circle and inside the board...
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A circle of radius 4 cm is carved with a sharp knife into 17 Jul 2006, 21:56
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Length of each side of the square = 100/4 = 25cm

The sum of the difference between the square of sides 25cm and 21 cm, and the difference between a circle of 12cm diameter and 8cm diameter will be the total area painted.

Painted area
= (25^2 - 21^2) + [(pi*6^2) - (pi*4^2)]
= 184 + 20pi

Percentage = (184 + 20pi)/25^2 * 100 = 39.5%

ywilfred,

the question says "within" 2 cm of the carved path of the circle but you assumed outside the edge of the carved path.

shouldn't the Percentage be = (25^2 - 21^2) + [(pi*4^2) - (pi*2^2)] =
(184 + 12pi)/25^2 * 100

kevincan
A circle of radius 4 cm is carved with a sharp knife into the middle of a square board that has a perimeter of 100cm. The portion of the board that is within 2 cm of either the edge of the board or the carved path of the circle is painted black. What percent of the entire board is painted black?

(A) 39.5% (B) 41.5% (C) 43.5% (D) 45.5% (E) 47.5%

Hmm.... good point.. I took the meaning 'within 2cm' to be anywhere 2cm outside of the circle or inside the board.... but I think you can take it the other way round and say 2cm inside the circle and inside the board...
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seems the question is not properly structured. if we take the values as per the information provided, the prob will be below 39.5% (however i have not calculated anything), which is not the AC.

hope kevin will take care of it.
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A circle of radius 4 cm is carved with a sharp knife into 17 Jul 2006, 23:52
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No, the question is fine. What makes you say the percentage will be so low?
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A circle of radius 4 cm is carved with a sharp knife into 18 Jul 2006, 06:33
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kevincan
No, the question is fine. What makes you say the percentage will be so low?
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if Painted area is 184 + 20pi, p = 39.5%.
if Painted area is 184 + 12pi, p = 35.47

imo, it should be 2nd one and in that case you need to update the ACs.



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