|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
18 Sep 2018, 21:57
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
33% (02:33) correct
67%
(02:35)
wrong
based on 60
sessions
History
Date
Time
Result
Not Attempted Yet
If a circle of radius length 4 and an equilateral triangle of side 4 are made to overlap as shown, what is the approximate area of the shaded region?
A. 1
B. 2
C. 4
D. 8
E. 16
Attachment:
image030.jpg [ 2.27 KiB | Viewed 3110 times ]
29 Aug 2021, 07:53
Kudos
Bookmarks
Bunuel
Since the radius has length 4, and the triangle has sides of length 4, we can see we have the following equilateral triangle in our diagram:
Since we have an equilateral triangle, each angle inside the triangle must be 60° as follows:
Now we'll find the area of the green sector below:
Area of sector \(=(\frac{60}{360})(\pi)(4^2)\)
\(=(\frac{1}{6})(\pi)(16)\)
Now we'll find the area of the red equilateral triangle below
We'll use the formula for the area of an equilateral triangle: Area \(= (\frac{\sqrt{3}}{4})(side^2)\)
\(= (\frac{\sqrt{3}}{4})(4^2)\)
\(= (\frac{\sqrt{3}}{4})(16)\)
\(= 4\sqrt{3}\)
The area of the shaded region = (area of green sector) - (area of red equilateral triangle)
\(=(\frac{1}{6})(\pi)(16)-4\sqrt{3}\)
\(≈(\frac{1}{6})(3.1)(16)-4(1.7)\)
\(≈8.3-6.8\)
\(≈1.5\)
Hmmmm, A or B both look good.
General Discussion
19 Sep 2018, 07:10
Kudos
Bookmarks
The required area is the
area of arc subtending 60 degree at center - area of equilateral triangle.
= (pi*4*4/6) - (3^0.5)*4*4/4
=1.44
So answer is A
area of arc subtending 60 degree at center - area of equilateral triangle.
= (pi*4*4/6) - (3^0.5)*4*4/4
=1.44
So answer is A
