[phpBB Debug] PHP Notice: in file /includes/check_new_recommended_questions.php on line 37: Undefined array key "last_recommended_questions_epoch"
[phpBB Debug] PHP Notice: in file /includes/check_new_recommended_questions.php on line 41: Undefined array key "last_recommended_questions_epoch"
In the figure above, AC = BC = 8, angle C = 90°, and the circular arc : Problem Solving (PS)
 Last visit was: 20 Jul 2024, 02:54 It is currently 20 Jul 2024, 02:54
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# In the figure above, AC = BC = 8, angle C = 90°, and the circular arc

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94426
Own Kudos [?]: 642450 [2]
Given Kudos: 86335
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30839 [2]
Given Kudos: 799
General Discussion
Manager
Joined: 05 Mar 2015
Status:A mind once opened never loses..!
Posts: 172
Own Kudos [?]: 676 [1]
Given Kudos: 258
Location: India
MISSION : 800
WE:Design (Manufacturing)
Manager
Joined: 26 Dec 2012
Posts: 132
Own Kudos [?]: 51 [1]
Given Kudos: 4
Location: United States
Concentration: Technology, Social Entrepreneurship
WE:Information Technology (Computer Software)
Re: In the figure above, AC = BC = 8, angle C = 90°, and the circular arc [#permalink]
1
Kudos
Area of shaded region = (area of circle/4) - area of triangle = (pi* 8^2)/4 - (8*8/4) = 16 pi - 32

Thanks,
Math Expert
Joined: 02 Sep 2009
Posts: 94426
Own Kudos [?]: 642450 [0]
Given Kudos: 86335
Re: In the figure above, AC = BC = 8, angle C = 90°, and the circular arc [#permalink]
Bunuel wrote:

In the figure above, AC = BC = 8, angle C = 90°, and the circular arc has its center at point C. Find the area of the shaded region.

A. $$8\pi-32$$
B. $$16\pi-32$$
C. $$16\pi-64$$
D. $$32\pi-32$$
E. $$32\pi-64$$

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

There’s not a single formula we can use to get the answer, but by combining a few formulas, we can calculate this.

First, think about the circle. The circle has radius r = 8, so its total area would be $$A=\pi{r^2}=64\pi$$.
gm-tuaaof_img5

This entire figure is a quarter of the circle, so that area would be $$quarter \ circle=16\pi$$.

Now, the shaded area (technically known as a circular segment), would have an area of
(circular segment) = (quarter circle) – (triangle ABC)

Well, we already have the area of the quarter circle. The triangle would have an area of (1/2)bh = 32. Therefore, the area of the segment is $$area=16\pi-32$$.