Last visit was: 26 Apr 2026, 06:04 It is currently 26 Apr 2026, 06:04
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
555-605 (Medium)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 26 Apr 2026
Posts: 109,836
Own Kudos:
811,360
Given Kudos: 105,893
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,836
Kudos: 811,360
The figure above is a cube with edges of length 9. Points C and D lie 07 Dec 2020, 01:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

75% (02:31) correct 25% (02:48) wrong based on 63 sessions

History

Date
Time
Result
Not Attempted Yet

The figure above is a cube with edges of length 9. Points C and D lie on diagonal AB such that points A, C, D, and B are equally spaced. As shown, a right circular cylindrical hole is cut out of the cube so that segment CD is a diameter of the top of the hole. What is the volume of the resulting figure?

A. \(729-162\pi\)

B. \(729-\frac{81\pi}{2}\)

C. \(729-81\pi\)

D. \(729-9\pi\)

E. \(729\)



Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

Show Spoiler
Attachment:
1.jpg
1.jpg [ 18.01 KiB | Viewed 3420 times ]
ShowHide Answer
Official Answer
B
User avatar
rajatchopra1994
User avatar
Joined: 16 Feb 2015
Last visit: 22 Jun 2024
Posts: 1,052
Own Kudos:
1,308
Given Kudos: 30
Location: United States
Posts: 1,052
Kudos: 1,308
The figure above is a cube with edges of length 9. Points C and D lie 07 Dec 2020, 05:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Explanation:

Diagonal AB = Side of Cube x √2 = 9√2
Diameter of Cylinder = 9√2/3 = 3√2 , r = 3√2/2
Area of Cylinder CD = π*r^2*h = π*(3√2/2)^2*9 = π*9x2x9/4 = 81π/2
Area of Cube = (side)^3 = 9^3 = 729

Resultant area = 729 - 81π/2

IMO-B
User avatar
Pankaj0901
User avatar
Joined: 18 Dec 2018
Last visit: 17 Dec 2022
Posts: 403
Own Kudos:
53
 [1]
Given Kudos: 737
Location: India
WE:Account Management (Hospitality and Tourism)
Posts: 403
Kudos: 53
 [1]
The figure above is a cube with edges of length 9. Points C and D lie 07 Dec 2020, 11:15
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
IMO answer B
Diagonal AB = 9√2
=> Diameter Cylinder = 9√2/3 = 3√2
=> radius = 3/√2
=> Area of Cylinder CD = π*r^2*h = π*((3/√2)^2)*9 = π*9x2x9/4 = 81π/2
Required area = 729 - 81π/2

Bunuel

The figure above is a cube with edges of length 9. Points C and D lie on diagonal AB such that points A, C, D, and B are equally spaced. As shown, a right circular cylindrical hole is cut out of the cube so that segment CD is a diameter of the top of the hole. What is the volume of the resulting figure?

A. \(729-162\pi\)

B. \(729-\frac{81\pi}{2}\)

C. \(729-81\pi\)

D. \(729-9\pi\)

E. \(729\)



Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

Show Spoiler
Attachment:
1.jpg
Show more
User avatar
akadiyan
User avatar
Retired Moderator
Joined: 31 May 2017
Last visit: 20 Jun 2025
Posts: 724
Own Kudos:
706
 [1]
Given Kudos: 53
Concentration: Technology, Strategy
Schools: IIMA PGPX'23 Bayes Said '23
Products:
My Reviews
Schools: IIMA PGPX'23 Bayes Said '23
Posts: 724
Kudos: 706
 [1]
The figure above is a cube with edges of length 9. Points C and D lie 07 Dec 2020, 21:34
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The figure above is a cube with edges of length 9. Points C and D lie on diagonal AB such that points A, C, D, and B are equally spaced. As shown, a right circular cylindrical hole is cut out of the cube so that segment CD is a diameter of the top of the hole. What is the volume of the resulting figure?

Side length of the cube = 9
Diagonal of a cube = Side \(\sqrt{2}\) = 9\(\sqrt{2}\)

The points A,C,D and B are equally placed , so consider the distance between any 2 points as x, so 3x = diagonal of the cube
3x = 9\(\sqrt{2}\)
x = \(\frac{9\sqrt{2} }{ 3}\) = 3\(\sqrt{2}\)
Diameter of the cylinder = 3\(\sqrt{2}\)
Radius of the cylinder = \(\frac{3\sqrt{2} }{ 2}\)

Area of cylinder = \(\pi* r^2 * h\) = \(\pi * (3\sqrt{2})^2*9\) = \(\frac{81 \pi }{ 2}\)

Area of cube = \(Side^3\) = \(9^3\) = 729

Volume = 729 - \(\frac{81 \pi }{ 2}\)

Ans: B
User avatar
exc4libur
User avatar
Joined: 24 Nov 2016
Last visit: 22 Mar 2022
Posts: 1,680
Own Kudos:
1,469
Given Kudos: 607
Location: United States
Posts: 1,680
Kudos: 1,469
The figure above is a cube with edges of length 9. Points C and D lie 08 Dec 2020, 06:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

The figure above is a cube with edges of length 9. Points C and D lie on diagonal AB such that points A, C, D, and B are equally spaced. As shown, a right circular cylindrical hole is cut out of the cube so that segment CD is a diameter of the top of the hole. What is the volume of the resulting figure?

A. \(729-162\pi\)

B. \(729-\frac{81\pi}{2}\)

C. \(729-81\pi\)

D. \(729-9\pi\)

E. \(729\)
Show more

cub-vol: 9^3=729
a-c-d-b=9V2, c-d=9V2/3=3V2
r=3V2/2, h=9
cyl-vol: pi.r^2*h=81/2.pi

(B)
Moderators:
Bunuel
Math Expert
109836 posts
Krunaal
Tuck School Moderator
852 posts