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In the figure above, a circle with center O touches three sides of a

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In the figure above, a circle with center O touches three sides of a [#permalink]

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New post 21 Nov 2017, 23:09
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In the figure above, a circle with center O touches three sides of a rectangle of length m and width n. Which of the following gives the area of the shaded region?

(A) πn^2/4
(B) mn – 2πn
(C) mn – πn^2
(D) mn – πn^2/2
(E) mn – πn^2/4

[Reveal] Spoiler:
Attachment:
2017-11-21_1031.png
2017-11-21_1031.png [ 3.95 KiB | Viewed 337 times ]
[Reveal] Spoiler: OA

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Re: In the figure above, a circle with center O touches three sides of a [#permalink]

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New post 21 Nov 2017, 23:22
E is answer
[(m*n)-{(3.14*(n^2)/4}]

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In the figure above, a circle with center O touches three sides of a [#permalink]

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New post 26 Nov 2017, 21:02
Bunuel wrote:
Image
In the figure above, a circle with center O touches three sides of a rectangle of length m and width n. Which of the following gives the area of the shaded region?

(A) πn^2/4
(B) mn – 2πn
(C) mn – πn^2
(D) mn – πn^2/2
(E) mn – πn^2/4

[Reveal] Spoiler:
Attachment:
2017-11-21_1031.png

Rectangle area = mn

The radius of the circle is \(\frac{1}{2}n\)

The area of the circle is
\(\pi r^2 = \pi* (\frac{1}{2}n)^2=\frac{n^2}{4}\pi\)

(Rectangle area) - (circle area) = Shaded area

Shaded area = \(mn - \frac{n^2}{4}\pi\)

Answer E

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Re: In the figure above, a circle with center O touches three sides of a [#permalink]

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New post 29 Nov 2017, 10:57
Bunuel wrote:
Image
In the figure above, a circle with center O touches three sides of a rectangle of length m and width n. Which of the following gives the area of the shaded region?

(A) πn^2/4
(B) mn – 2πn
(C) mn – πn^2
(D) mn – πn^2/2
(E) mn – πn^2/4

[Reveal] Spoiler:
Attachment:
2017-11-21_1031.png


We see that the area of the shaded region is the difference between the area of the rectangle and the area of the circle. Since the width of the rectangle is n, we see that n is also the diameter of the circle. Thus, the radius of the circle is n/2.

Area of the rectangle = m x n = mn

Area of the circle = π x (n/2)^2 = π x (n^2/4) = πn^2/4

Thus, the area of the shaded region = mn - πn^2/4.

Answer: E
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Kudos [?]: 1011 [0], given: 3

Re: In the figure above, a circle with center O touches three sides of a   [#permalink] 29 Nov 2017, 10:57
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