GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Oct 2018, 03:26

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If each curved side in the figure above is a semicircle with radius 20

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50007
If each curved side in the figure above is a semicircle with radius 20  [#permalink]

### Show Tags

16 Nov 2017, 01:49
00:00

Difficulty:

25% (medium)

Question Stats:

85% (01:24) correct 15% (01:31) wrong based on 34 sessions

### HideShow timer Statistics

If each curved side in the figure above is a semicircle with radius 20, and the two parallel sides each have length 100, what is the area of the region by the above figure?

(A) 2,000
(B) 4,000
(C) 2000 – 200π
(D) 4,000 – 200π
(E) 4000 – 400 π

Attachment:

2017-11-16_1237.png [ 3.19 KiB | Viewed 722 times ]

_________________
Intern
Joined: 08 Aug 2017
Posts: 11
Re: If each curved side in the figure above is a semicircle with radius 20  [#permalink]

### Show Tags

16 Nov 2017, 04:32
B.
area of the rectangle is = 40*100 = 4000
area of semicircle is = 1/2 * pi*20*20 = 200pi
now, area of the entire thing is = 4000-200pi+200pi = 4000
hence, B.
Manager
Joined: 22 May 2017
Posts: 113
Re: If each curved side in the figure above is a semicircle with radius 20  [#permalink]

### Show Tags

16 Nov 2017, 09:02
observe the figure ,
below semi circle is equal to semi circle cut out above ( r is equal)
only find the area of rectangle 40*100 = 4000
_________________

-------------------------------------------------------------------------------------------------
Don't stop when you are tired , stop when you are DONE .

Manager
Joined: 13 Jun 2012
Posts: 190
Location: United States
WE: Supply Chain Management (Computer Hardware)
If each curved side in the figure above is a semicircle with radius 20  [#permalink]

### Show Tags

16 Nov 2017, 09:10
The answer should be 4000 (A) Width is 2R= 20*2

area of rectangle L*B= 100*40= 4000. Now a semi circle is inside the rectangle and one is outside where both have same radius so each cancels out and the area of the figure is 4000.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3896
Location: United States (CA)
Re: If each curved side in the figure above is a semicircle with radius 20  [#permalink]

### Show Tags

17 Nov 2017, 14:33
Bunuel wrote:

If each curved side in the figure above is a semicircle with radius 20, and the two parallel sides each have length 100, what is the area of the region by the above figure?

(A) 2,000
(B) 4,000
(C) 2000 – 200π
(D) 4,000 – 200π
(E) 4000 – 400 π

Attachment:
2017-11-16_1237.png

We will use a method called “cut and paste.” We see that we can cut the bottom semicircle out and paste it to the top so that the entire figure becomes a rectangle. The length of the rectangle will be 100 and the width will be the diameter or the semicircle, which is 40. Thus, the area of the rectangle, or the figure, is 100 x 40 = 4,000.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If each curved side in the figure above is a semicircle with radius 20 &nbs [#permalink] 17 Nov 2017, 14:33
Display posts from previous: Sort by