NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 06:20 It is currently 24 Apr 2024, 06:20
Decision Tracker
My Rewards
New posts
New comers' posts

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

As the figure shows, a ball and cone are inscribed by a cylinder. What

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
Own Kudos [?]: 16594 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
As the figure shows, a ball and cone are inscribed by a cylinder. What [#permalink] New post   05 Aug 2019, 01:19
1
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

62% (02:33) correct 38% (03:00) wrong based on 68 sessions
Hide Show timer Statistics
[GMAT math practice question]

As the figure shows, a ball and cone are inscribed by a cylinder. What is the ratio of the volumes of the sphere to the cone to the cylinder?

Attachment:
8.5 PS.png
8.5 PS.png [ 57.4 KiB | Viewed 1563 times ]


\(A. 1:1:2\)

\(B. 1.5:1:3\)

\(C. 1.5:1.5:2\)

\(D. 2:1:3\)

\(E. 3:2:4\)
ShowHide Answer
Official Answer
D
User avatar
L
TheNightKing
VP
VP
Joined: 18 Dec 2017
Posts: 1170
Own Kudos [?]: 991 [1]
Given Kudos: 421
Location: United States (KS)
GMAT 1: 600 Q46 V27
Send PM
Re: As the figure shows, a ball and cone are inscribed by a cylinder. What [#permalink] New post   11 Aug 2019, 16:31
1
Kudos
MathRevolution wrote:
[GMAT math practice question]

As the figure shows, a ball and cone are inscribed by a cylinder. What is the ratio of the volumes of the sphere to the cone to the cylinder?

Attachment:
8.5 PS.png


\(A. 1:1:2\)

\(B. 1.5:1:3\)

\(C. 1.5:1.5:2\)

\(D. 2:1:3\)

\(E. 3:2:4\)


If you know for a fact that volume of a cone is 1/3rd of the volume of the cylinder then you can just compare ratios.
In case of D, Cylinder is 3/6 which is 1/2.
1/3 of 1/2 is 1/6. Option D satisfies that.
Hence D.

I got it right but I did not approach it correctly.
User avatar
S
Karmesh
Manager
Manager
Joined: 18 Apr 2019
Posts: 68
Own Kudos [?]: 96 [0]
Given Kudos: 86
Location: India
Schools: IESE '22 CEIBS '22 (II)
GMAT 1: 720 Q48 V40
GPA: 4
Send PM
Re: As the figure shows, a ball and cone are inscribed by a cylinder. What [#permalink] New post   05 Aug 2019, 04:38
This question is pretty straight forward if you know the formulas and realize that the diameter of the sphere is equal to the height of the cone and cylinder.

Vol of sphere : 4/3*(pi)*r^3

Vol of cone : 1/3*pi*r^2*h

Vol of cylinder : pi*r^2*h

pi and r^2 pretty much cancel right away. 2r = h (as mentioned above)
therefore, we get - 2:1:3
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
Own Kudos [?]: 16594 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: As the figure shows, a ball and cone are inscribed by a cylinder. What [#permalink] New post   07 Aug 2019, 03:15
Expert Reply
=>

From the figure, the radii of the sphere and the base circle are \((\frac{9}{2})\).

The volume of the sphere is \((\frac{4}{3}) π(\frac{9}{2})^3 = π(\frac{243}{2}).\)

The volume of the cone is \((\frac{1}{3}) π(\frac{9}{2})^2(9) = π(\frac{243}{4}).\)

The volume of the cylinder is \(π(\frac{9}{2})^2(9) = π(\frac{729}{4})\)

Thus, the volumes are in the ratio \(π(\frac{243}{2}) : π(\frac{243}{4}) : π(\frac{729}{4}) = 2 : 1 : 3.\)

Therefore, the answer is D.
Answer: D
GMAT Club Bot
gmatclubot
Re: As the figure shows, a ball and cone are inscribed by a cylinder. What [#permalink]
07 Aug 2019, 03:15
Moderators:
Bunuel
Math Expert
92901 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions