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

 It is currently 15 Jun 2019, 21:56

### 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

# In the figure above, if radius OA is 8 and the area of right triangle

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55609
In the figure above, if radius OA is 8 and the area of right triangle  [#permalink]

### Show Tags

10 Jan 2019, 02:29
00:00

Difficulty:

35% (medium)

Question Stats:

74% (02:21) correct 26% (02:06) wrong based on 24 sessions

### HideShow timer Statistics

In the figure above, if radius OA is 8 and the area of right triangle OAB is 32, what is the area of the shaded region?

A. 64π + 32
B. 60π + 32
C. 56π + 32
D. 32π + 32
E. 16π + 32

Attachment:

2019-01-10_1328.png [ 17.67 KiB | Viewed 402 times ]

_________________
Manager
Joined: 01 May 2017
Posts: 82
Location: India
Re: In the figure above, if radius OA is 8 and the area of right triangle  [#permalink]

### Show Tags

10 Jan 2019, 03:15
In the figure above, if radius OA is 8 and the area of right triangle OAB is 32, what is the area of the shaded region?

Area of the circle = Pi*8^2
= $$64*Pi$$

Area of the right triangle = 32

Since Angle OAB = 90 degrees
and $$1/2*AB*OA$$ = 32 (Given OA = radius of circle = 8)
implies AB = 8
implies AB = OA = 8, OAB is right isosceles triangle with AOB = OBA = 45 degrees

Area of the part of the circle excluding the right triangle = $$((360 - 45)/360)*64*PI$$
= $$56*PI$$
Total shaded region = $$56*Pi + 32$$
Option C is correct
CEO
Joined: 18 Aug 2017
Posts: 3834
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In the figure above, if radius OA is 8 and the area of right triangle  [#permalink]

### Show Tags

10 Jan 2019, 05:56
Bunuel wrote:

In the figure above, if radius OA is 8 and the area of right triangle OAB is 32, what is the area of the shaded region?

A. 64π + 32
B. 60π + 32
C. 56π + 32
D. 32π + 32
E. 16π + 32

Attachment:
2019-01-10_1328.png

given area of circle = 64pi
and side ab = 0.5*oa*ab= 32
ab= 8
so we can say that oa=ab= 8 and triangel oab is 45:45;90 triangle and angle AOB is 45
so area of side AOC ' c is point on circumference on length ob'
45/360* pi * 8 * 8 = 8 pi

so total area of the figure : 64pi-8pi + 32
; 56pi+32 IMO C
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
VP
Joined: 09 Mar 2018
Posts: 1004
Location: India
Re: In the figure above, if radius OA is 8 and the area of right triangle  [#permalink]

### Show Tags

10 Jan 2019, 06:43
Bunuel wrote:

In the figure above, if radius OA is 8 and the area of right triangle OAB is 32, what is the area of the shaded region?

Attachment:
2019-01-10_1328.png

Area of Triangle OAB
=> 1/2 OA * AB = 32
=> AB = 8

From this we can say that triangle OAB is 45-45-90, implying < AOB = 45

To calculate the area of the inner sector(one which doesn't include the triangle OAB), for the formula $$\frac{theta}{360}$$* π $$r^2$$
We can caluclaet the theta by 360-45 = 315
Now, $$\frac{315}{360}$$* π $$8^2$$
=> 56 π

Total Area will be 56 π + 32

_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Re: In the figure above, if radius OA is 8 and the area of right triangle   [#permalink] 10 Jan 2019, 06:43
Display posts from previous: Sort by