It is currently 26 Mar 2019, 05:25

### 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

Author Message
TAGS:
Moderator
Joined: 18 Apr 2015
Posts: 5919
Followers: 96

Kudos [?]: 1158 [0], given: 5494

If each curved side in the figure above is a semicircle with [#permalink]  20 Jun 2018, 09:35
Expert's post
00:00

Question Stats:

83% (00:58) correct 16% (00:44) wrong based on 12 sessions
Attachment:

semi.jpg [ 30.65 KiB | Viewed 382 times ]

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 shaded region?

(A) $$2,000$$

(B) $$4,000$$

(C) $$2,000 - 200\pi$$

(D) $$4,000 - 200\pi$$

(E) $$4,000 - 400\pi$$
[Reveal] Spoiler: OA

_________________
Director
Joined: 20 Apr 2016
Posts: 828
WE: Engineering (Energy and Utilities)
Followers: 11

Kudos [?]: 605 [0], given: 124

Re: If each curved side in the figure above is a semicircle with [#permalink]  23 Jun 2018, 07:37
Carcass wrote:
Attachment:
The attachment semi.jpg is no longer available

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 shaded region?

(A) $$2,000$$

(B) $$4,000$$

(C) $$2,000 - 200\pi$$

(D) $$4,000 - 200\pi$$

(E) $$4,000 - 400\pi$$

Here,
Let us calculate the whole figure as one with 2 semicircle(1 shaded in red and other in black) and 1 rectangle (Please refer to the picture attached) and then after calculating the area's of each one of them we can deduct the semicircle (shaded in red)which will left us with the area of the shaded region
First let us calculate the area of the semicircle = $$\pi r^2$$/2

therefore the area of the semicircle down =$$200\pi$$ and the semicircle of the top (red shaded) =$$200\pi$$

and the area of the circle

Now the area of the rectangle (including the semicircle red shaded)= L *B

we know Length = 100

Therefore the area = 100 * 40 = 4000

Now the area of the shaded region only= 4000 + $$200\pi$$(semi circle shaded in black) -$$200\pi$$(semi circle shaded in red) = 4000
Attachments

Untitled.png [ 55.32 KiB | Viewed 347 times ]

_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting https://greprepclub.com/forum/rules-for ... -1083.html

Re: If each curved side in the figure above is a semicircle with   [#permalink] 23 Jun 2018, 07:37
Display posts from previous: Sort by

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

 Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.