It is currently 20 Mar 2019, 05:31

### 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

# If a solid metal cylinder with radius 3 and height 12

Author Message
TAGS:
GRE Instructor
Joined: 10 Apr 2015
Posts: 1525
Followers: 55

Kudos [?]: 1455 [1] , given: 8

If a solid metal cylinder with radius 3 and height 12 [#permalink]  23 Jul 2018, 13:38
1
KUDOS
Expert's post
00:00

Question Stats:

90% (01:48) correct 10% (00:56) wrong based on 10 sessions
If a solid metal cylinder with radius 3 and height 12 is melted and then formed into a solid sphere, what is the radius of the sphere?
Note: Volume of sphere = (4/3)(π)(radius³)

A) ∛6
B) ∛12
C) ∛36
D) 3
E) 3∛3
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Director
Joined: 20 Apr 2016
Posts: 824
WE: Engineering (Energy and Utilities)
Followers: 10

Kudos [?]: 601 [1] , given: 121

Re: If a solid metal cylinder with radius 3 and height 12 [#permalink]  24 Jul 2018, 00:00
1
KUDOS
GreenlightTestPrep wrote:
If a solid metal cylinder with radius 3 and height 12 is melted and then formed into a solid sphere, what is the radius of the sphere?
Note: Volume of sphere = (4/3)(π)(radius³)

A) ∛6
B) ∛12
C) ∛36
D) 3
E) 3∛3

Volume of cylinder = $$\pi * {Radius}^2 * Height = \pi * 3^2 * 12 = 108\pi$$

Now Volume of cylinder = Volume of sphere (Since the cylinder is melted to made sphere)

or $$108\pi = 4/3 * \pi * {Radius}^3$$

or $${Radius}^3 = 81$$

or Radius of Sphere = $$3∛3$$
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting https://greprepclub.com/forum/rules-for ... -1083.html

GRE Instructor
Joined: 10 Apr 2015
Posts: 1525
Followers: 55

Kudos [?]: 1455 [0], given: 8

Re: If a solid metal cylinder with radius 3 and height 12 [#permalink]  25 Jul 2018, 06:25
Expert's post
GreenlightTestPrep wrote:
If a solid metal cylinder with radius 3 and height 12 is melted and then formed into a solid sphere, what is the radius of the sphere?
Note: Volume of sphere = (4/3)(π)(radius³)

A) ∛6
B) ∛12
C) ∛36
D) 3
E) 3∛3

Key concept: the volume of the cylinder = the volume of the sphere

volume of the cylinder = πr²h
= π(3²)(12)
= 108π

So, the volume of the sphere = 108π
Divide both sides by π to get: (4/3)(radius³) = 108
Multiply both sides by 3 to get: (4)(radius³) = 324
Divide both sides by 4 to get: radius³ = 81
Check the answer choices....not there! Looks like we need to simplify ∛81
Notice that 81 = 27 x 3
So, ∛81 = ∛27 x ∛3
= 3 x ∛3
= 3∛3

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: If a solid metal cylinder with radius 3 and height 12   [#permalink] 25 Jul 2018, 06:25
Display posts from previous: Sort by