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

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Math Expert
Joined: 02 Sep 2009
Posts: 62499
Two equal circles are cut out of a rectangle of card of dimensions 16  [#permalink]

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14 May 2016, 02:53
00:00

Difficulty:

25% (medium)

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 [ 1.54 KiB | Viewed 5373 times ]

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Math Expert
Joined: 02 Aug 2009
Posts: 8308
Re: Two equal circles are cut out of a rectangle of card of dimensions 16  [#permalink]

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14 May 2016, 02:57
Bunuel wrote:

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..

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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14 May 2016, 07:17
Bunuel wrote:

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 [ 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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Thanks and Regards

Abhishek....

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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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