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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, 01:10
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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) \(32 + 2\pi\)


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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 02 Aug 2016, 14:04
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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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Re: The window in the figure above consists of a rectangle and a semicircl  [#permalink]

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New post 18 Jun 2016, 04:36
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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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Re: The window in the figure above consists of a rectangle and a semicircl  [#permalink]

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New post 18 Jun 2016, 05:04
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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 22436 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, 01:09
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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Re: The window in the figure above consists of a rectangle and a semicircl  [#permalink]

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New post Updated on: 17 Sep 2016, 03:37
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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Originally posted by LogicGuru1 on 19 Jun 2016, 03:05.
Last edited by LogicGuru1 on 17 Sep 2016, 03:37, 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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New post 16 Sep 2016, 23:00
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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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Re: The window in the figure above consists of a rectangle and a semicircl  [#permalink]

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New post 16 Sep 2016, 23:54
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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Re: The window in the figure above consists of a rectangle and a semicircl  [#permalink]

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New post 11 Oct 2016, 01:28
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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Re: The window in the figure above consists of a rectangle and a semicircl  [#permalink]

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New post 05 Aug 2017, 04:23
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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Re: The window in the figure above consists of a rectangle and a semicircl  [#permalink]

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New post 19 Dec 2017, 06:42
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\(\pi\)


We are given a semicircle with a diameter of 4 ft., which also represents the width of the rectangle. We are also given that height of the window is 10 ft., which is the combined length of the radius of the semicircle and the length of the rectangle. To determine the length of the rectangle, we can subtract the radius of the semicircle, which is 2 ft., from the total length of 10 ft.:

10 - 2 = 8 ft.

Now we can calculate the area of the semicircle and the rectangle.

Area of semicircle = (1/2)π(2^2) = 2π

Area of rectangle = 8 x 4 = 32

Thus, the total area is 32 + 2π.

Answer: E
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New post 03 Jul 2020, 06:39
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) \(32 + 2\pi\)


We need understand that the figure is composed of a semicircle and a rectangle.

Area of the semicircle would be pi*radius^2/2=2 pi

We need to next find the area of the rectangle, the radius of circle will be 2 all throughout therefore we can find the length of the rectangle, which is 10-2=8.

Area of rectangle =8*4=32

Area of the figure = \(32 + 2\pi\) . E
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The window in the figure above consists of a rectangle and a semicircl   [#permalink] 03 Jul 2020, 06:39

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

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