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Two equal circles are cut out of a rectangle of card of dimensions 16

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Two equal circles are cut out of a rectangle of card of dimensions 16  [#permalink]

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New post 14 May 2016, 02:53
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Question Stats:

92% (01:54) correct 8% (01:49) wrong based on 25 sessions

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Two equal circles are cut out of a rectangle of card of dimensions 16 by 8. The circles have the maximum diameter possible. What is the approximate area of the paper remaining after the circles have been cut out?

A. 104
B. 78
C. 54
D. 27
E. 13

Attachment:
2016-05-14_1451.png
2016-05-14_1451.png [ 1.54 KiB | Viewed 5373 times ]

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Re: Two equal circles are cut out of a rectangle of card of dimensions 16  [#permalink]

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New post 14 May 2016, 02:57
Bunuel wrote:
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Two equal circles are cut out of a rectangle of card of dimensions 16 by 8. The circles have the maximum diameter possible. What is the approximate area of the paper remaining after the circles have been cut out?

A. 104
B. 78
C. 54
D. 27
E. 13

Attachment:
2016-05-14_1451.png


As the two circles are max possible and are equal....
tey will have diameter of 8..

AREA of rectangle = \(16*8 = 128\)
AREA of two circles = \(2* pi * r^2 = 2pi*4^2 = 32pi = 32*3.1 = 100\) approx..

the choices are too spread to worry about decimal...

ans \(= 128-100 = 28\), this is closer to 27..
D
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Re: Two equal circles are cut out of a rectangle of card of dimensions 16  [#permalink]

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New post 14 May 2016, 07:17
Bunuel wrote:
Image
Two equal circles are cut out of a rectangle of card of dimensions 16 by 8. The circles have the maximum diameter possible. What is the approximate area of the paper remaining after the circles have been cut out?

A. 104
B. 78
C. 54
D. 27
E. 13

Attachment:
The attachment 2016-05-14_1451.png is no longer available

Attachment:
2016-05-14_1451.png
2016-05-14_1451.png [ 4.03 KiB | Viewed 4158 times ]


Area of the rectangle is 16 x 8 = 128

Area of 2 circle is \(2*\frac{22}{7}*4*4\) ~ 100

Area of the remaining shape is 128 - 100 => 28

Hence answer will be (D) 28
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Re: Two equal circles are cut out of a rectangle of card of dimensions 16   [#permalink] 14 May 2016, 07:17
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