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OG Rectangle and Semicircle Q

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by AbeNeedsAnswers » Wed Jul 19, 2017 10:12 pm
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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 + 8ππ
B) 40 + 2ππ
C) 32 + 8ππ
D) 32 + 4ππ
E) 32 + 2Ï€

E
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by Jay@ManhattanReview » Wed Jul 19, 2017 11:45 pm
AbeNeedsAnswers 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 + 8ππ
B) 40 + 2ππ
C) 32 + 8ππ
D) 32 + 4ππ
E) 32 + 2Ï€

E
The area of the window = Area of the semi-circle + Area of the rectangle

Area of the semi-circle = Half of the Area of the circle

It is given that the diameter of the semi-circle = 4 feet, thus the radius = 2 feet

Area of the semi-circle = 1/2*(Ï€r^2) = 1/2*(Ï€*2^2) = 2Ï€ sq feet

Area of the rectangle = Length x Breadth

It is given that Breadth = 4 feet and that the length + radius of the semi-circle = 10 feet.

Thus, the length of the rectangle = 10 - 2 = 8 feet

Thus, Area of the rectangle = Length x Breadth = 8 x 4 = 32 sq feet

=> The area of the window = Area of the semi-circle + Area of the rectangle = [spoiler]2Ï€ + 32 sq feet[/spoiler]

The correct answer: D

Hope this helps!

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-Jay
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by [email protected] » Thu Jul 20, 2017 11:39 am
Hi AbeNeedsAnswers,

While there is a formal 'math' approach to this question - and the Official Explanation will provide it, there's a great way to use the answers against the prompt and minimize the work a little bit (as long as you know that the approximate value of pi = 3.14).

Since the window is NOT a gigantic rectangle, the area would have to be LESS than (10)(4) = 40, so we can eliminate Answers A and B immediately. Taking that idea a step further, you should be able to estimate the values of the remaining 3 answer choices (again, use pi = 3.14 as an approximation).

In Answer D: 32 + 4pi would be about 32 + 4(3.14) = 32 + 12.56 = 44.56... but this is greater than 40. Answer C would be even greater than Answer D (since 8pi is greater than 4pi), so neither of those answers can possibly be correct. That leaves just one option...

Final Answer: E

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by Brent@GMATPrepNow » Mon Jul 24, 2017 12:02 pm
I just want to add to Rich's explanation by saying....
The diagrams in problem solving questions are DRAWN TO SCALE unless stated otherwise.

So, as Rich has demonstrated, we can use this fact to solve the question through estimation.

Cheers,
Brent
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by Jeff@TargetTestPrep » Tue Jul 25, 2017 11:03 am
AbeNeedsAnswers 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 + 8ππ
B) 40 + 2ππ
C) 32 + 8ππ
D) 32 + 4ππ
E) 32 + 2Ï€
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)Ï€(2^2) = 2Ï€

Area of rectangle = 8 x 4 = 32

Thus, the total area is 32 + 2Ï€.

Answer: E

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[email protected]

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