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The window in the figure above consists of a rectangle and a semicircl

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The window in the figure above consists of a rectangle and a semicircl [#permalink]

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New post 15 Jun 2016, 02:10
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The window in the figure above consists of a rectangle and a semicircle with dimensions as shown. What is the area, in square feet, of the window?

A) 40 + 8\(\pi\)
B) 40 + 2\(\pi\)
C) 32 + 8\(\pi\)
D) 32 + 4\(\pi\)
E) 32 + 2\(\pi\)
[Reveal] Spoiler: OA

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Re: The window in the figure above consists of a rectangle and a semicircl [#permalink]

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AbdurRakib wrote:
Image

The window in the figure above consists of a rectangle and a semicircle with dimensions as shown. What is the area, in square feet, of the window?

A) 40 + 8\(\pi\)
B) 40 + 2\(\pi\)
C) 32 + 8\(\pi\)
D) 32 + 4\(\pi\)
E) 32 + 2\(\pi\)



Let the height of the semi-circle be x. The height is same as the radius of the semi-circle.

Now consider the height of the rectangle as 10-x.

Given diameter of the circle is 4 and we get the radius as 2.

=> We get the height of the rectangle as 10-2 = 8. Now the area of the rectangle is 8 * 4 = 32.

The area of the semi circle is \(\pi\) * r^2 / 2.
=> \(\pi\) * 4 / 2 => \(\pi\) * 2 ( or ) 2\(\pi\).

Finally the sum of the areas of rectangle + semi circle is 32 + 2\(\pi\).
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AbdurRakib wrote:
Image

The window in the figure above consists of a rectangle and a semicircle with dimensions as shown. What is the area, in square feet, of the window?

A) 40 + 8\(\pi\)
B) 40 + 2\(\pi\)
C) 32 + 8\(\pi\)
D) 32 + 4\(\pi\)
E) 32 + 2\(\pi\)

Attachment:
vaxpj.jpg
vaxpj.jpg [ 33.73 KiB | Viewed 4406 times ]

Since the top part is a Semicircle , its area will be\(\frac{1}{2}\)*\(\pi\) *\(2^2\) = 2\(\pi\)

Area of the rectangle will be 8*4 =32

So, Total area is 32+ 2\(\pi\)

Answer will be (E)

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Re: The window in the figure above consists of a rectangle and a semicircl [#permalink]

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New post 19 Jun 2016, 02:09
How do you guys type pi? :shock:

The rectangle is 32, and the semi-circle is half of 4pi. So the answer is 32 + 2pi.

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HiLine wrote:
How do you guys type pi? :shock:

The rectangle is 32, and the semi-circle is half of 4pi. So the answer is 32 + 2pi.


\(\pi\): write \pi, mark and press m button.

Check for more here: rules-for-posting-please-read-this-before-posting-133935.html#p1096628

Hope it helps.
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The window in the figure above consists of a rectangle and a semicircl [#permalink]

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New post 19 Jun 2016, 04:05
Area of the semicircle = \(\frac{\pi r^2}{2}\)
Since Radius is 2 therefore Area of the semicircle =>\(\frac{\pi*2*2}{2}\)===> \(2\pi\)
Area of the rectangle=\(l . b = 8 x 4 = 32\)

total area = \(32 + 2\pi\)
Answer is E

AbdurRakib wrote:
Image

The window in the figure above consists of a rectangle and a semicircle with dimensions as shown. What is the area, in square feet, of the window?

A) 40 + 8\(\pi\)
B) 40 + 2\(\pi\)
C) 32 + 8\(\pi\)
D) 32 + 4\(\pi\)
E) 32 + 2\(\pi\)

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Last edited by LogicGuru1 on 17 Sep 2016, 04:37, edited 1 time in total.

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Re: The window in the figure above consists of a rectangle and a semicircl [#permalink]

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Here are a couple of videos about this problem. The first goes over a shortcut method to solve the question in a few seconds. The second goes over a more conventional, but more versatile, approach.

Shortcut method:



Conventional method:

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I see this differently.
If this was purely a rectangle, then the area would be 40sq.f

So A and B are automatically wrong.
Say I don't remember my geometry and only know that pi is 3.14, then everything is easy.
C=32+8*3.14=too much
D=32+4*3.14=too much

So by elimination the answer is E

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New post 17 Sep 2016, 00:54
area of semicircle = 2πr/2 = 2π
height of semi circle = 2
so l=8 b=4
lb = 32
window = 32 + 2π

E

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New post 11 Oct 2016, 02:28
lololol650 wrote:
I see this differently.
If this was purely a rectangle, then the area would be 40sq.f

So A and B are automatically wrong.
Say I don't remember my geometry and only know that pi is 3.14, then everything is easy.
C=32+8*3.14=too much
D=32+4*3.14=too much

So by elimination the answer is E


Did it the same way.

Half-circle --> 2/pi, we can narrow down the choices to two.
If it would be a full rectangle --> 4 * 10 = 40. But it is not a full rectangle.
--> Must be E.

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The window in the figure above consists of a rectangle and a semicircl [#permalink]

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New post 05 Aug 2017, 05:23
Estimate Shortcut:

If it were a rectangle of 4 x 10 then the area would be 40. But we chip of some area to make it a semicircle. Thus actual area is less than 40.

Pi = 3 (approx)

All answers except E are bigger than 40, we need something smaller than 40

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The window in the figure above consists of a rectangle and a semicircl   [#permalink] 05 Aug 2017, 05:23
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