GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
If each curved side in the figure above is a semicircle with
[#permalink]
20 Jun 2018, 09:35
20 Jun 2018, 09:35
2
Expert Reply
2
Bookmarks
00:00
Question Stats:
73% (01:07) correct
26% (01:20) wrong based on 94 sessions
Hide Show timer Statistics
Attachment:
semi.jpg [ 30.65 KiB | Viewed 6017 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) \(4,000 - 400\pi\)
Re: If each curved side in the figure above is a semicircle with
[#permalink]
23 Jun 2018, 07:37
23 Jun 2018, 07:37
2
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
here radius = 20
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
And Breadth = 40 since the radius given as 20
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 5942 times ]
Re: If each curved side in the figure above is a semicircle with
[#permalink]
04 Feb 2020, 09:55
04 Feb 2020, 09:55
2
No need to do hard calculation. Just Place the lower portion on the upper side. Then it becomes a complete rectangle.
Here, radius = 20, so diameter = 40 which is the width or other side of the rectangle. On the other hand the parallel side = 100.
Then, area of the rectangle = 40 X 100 = 4000.
Ans: B
Here, radius = 20, so diameter = 40 which is the width or other side of the rectangle. On the other hand the parallel side = 100.
Then, area of the rectangle = 40 X 100 = 4000.
Ans: B
