Join us for MBA Spotlight – The Top 20 MBA Fair      Schedule of Events | Register

It is currently 06 Jun 2020, 01:11

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.

Close

Request Expert Reply

Confirm Cancel

The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 23 Apr 2014
Posts: 3
The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere  [#permalink]

Show Tags

New post Updated on: 17 May 2016, 00:38
4
1
48
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

70% (02:36) correct 30% (02:34) wrong based on 519 sessions

HideShow timer Statistics

Image
The volume of a sphere with radius r is \(\frac {4}{3} \pi r^3\). A solid sphere of radius r that is made of a certain material weighs 40 pounds. The figure above shows half of a spherical shell made of the same material. What is the weight, in pounds, of the entire spherical shell if the outer radius is 5r and the inner radius is 2r?

A. 120
B. 360
C. 840
D. 1,080
E. 4,680

Attachment:
Untitled.png
Untitled.png [ 2.03 KiB | Viewed 50663 times ]
Attachment:
GmatPrepImage.png
GmatPrepImage.png [ 19.81 KiB | Viewed 39998 times ]

Originally posted by srmessi on 16 May 2016, 23:14.
Last edited by Bunuel on 17 May 2016, 00:38, edited 2 times in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8632
The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere  [#permalink]

Show Tags

New post 16 May 2016, 23:29
11
8
srmessi wrote:
Can any1 help me with This


Hi,

the V = \(\frac{4}{3}pi*r^3\) and this volume weighs 40 pounds...

If it is a shell, you can find V of solid part by subtracting inner empty sphere from total..
V of entire sphere \(\frac{4}{3} * pi *(5r)^3\)and V of inner empty space = \(\frac{4}{3} * pi *(2r)^3\)..

so V of solid =\(\frac{4}{3} * pi *(5r)^3 - \frac{4}{3}* pi *(2r)^3........................ = \frac{4}{3}*pi*r^3*(125-8)....................... = \frac{4}{3}pi*r^3*117\)

NOW \(\frac{4}{3}pi*r^3\) weighs 40 pounds,
so \(\frac{4}{3}pi*r^3*117\) will weigh \(40*117 = 4680\)...

E
_________________
Most Helpful Community Reply
VP
VP
User avatar
V
Status: Learning
Joined: 20 Dec 2015
Posts: 1088
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
GPA: 3.4
WE: Engineering (Manufacturing)
Reviews Badge CAT Tests
Re: The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere  [#permalink]

Show Tags

New post 01 Dec 2017, 07:04
12
1
A very tricky question
The answer is E
Weight of the sphere with radius r is =40
Now the radius of the outer shell =5r if we consider it as sphere then its weight would be 125 times 40=5000
Now the sphere with inner radius 2r will have 8 times 40 as weight =320
Subtract the weight ans we get the weight of the shell =5000-320=4680
General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64317
The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere  [#permalink]

Show Tags

New post 17 May 2016, 00:46
1
5
srmessi wrote:
Image
The volume of a sphere with radius r is \(\frac {4}{3} \pi r^3\). A solid sphere of radius r that is made of a certain material weighs 40 pounds. The figure above shows half of a spherical shell made of the same material. What is the weight, in pounds, of the entire spherical shell if the outer radius is 5r and the inner radius is 2r?

A. 120
B. 360
C. 840
D. 1,080
E. 4,680

Attachment:
Untitled.png
Attachment:
GmatPrepImage.png


23. Geometry




24. Coordinate Geometry




25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations



_________________
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 5021
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere  [#permalink]

Show Tags

New post 17 May 2016, 07:14
srmessi wrote:
Image
The volume of a sphere with radius r is \(\frac {4}{3} \pi r^3\). A solid sphere of radius r that is made of a certain material weighs 40 pounds. The figure above shows half of a spherical shell made of the same material. What is the weight, in pounds, of the entire spherical shellif the outer radius is 5r and the inner radius is 2r?

A. 120
B. 360
C. 840
D. 1,080
E. 4,680

Attachment:
The attachment Untitled.png is no longer available
Attachment:
The attachment GmatPrepImage.png is no longer available


\(\frac {4}{3} \pi r^3\) = \(40\)

\(\frac{22}{7} r^3\) = \(30\)

\(\frac{11}{7} r^3\) = \(15\)

\(r^3\) = \(15*7/11\)

Now think about the semi circle

Attachment:
Circle.PNG
Circle.PNG [ 13.33 KiB | Viewed 39672 times ]


So, Volume will be = \(\frac{2}{3}*\frac{22}{7}*( 5r^3 - 2r^3)\)

Or Volume = \(\frac{2}{3}*\frac{22}{7}*( 117r^3)\)

We know r^3 = \(15*7/11\) ; so substitute it ....

Volume = \(\frac{4}{3}*\frac{22}{7}*( 117*15*\frac{7}{11})\) ( Check the highlighted part in the question we require the volume of the complete sphere )

Volume = 4,680

You may ask the question why the question mentions

Quote:
The figure above shows half of a spherical shell


It's given only to show that the thickness of the spherical ball (which is hollow from inside )

Hence I completely endorse answer option (E)
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Intern
Intern
avatar
B
Joined: 09 Dec 2013
Posts: 26
Re: The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere  [#permalink]

Show Tags

New post 23 Jul 2017, 05:04
chetan2u wrote:
srmessi wrote:
Can any1 help me with This


Hi,

the V = \(\frac{4}{3}pi*r^3\) and this volume weighs 40 pounds...

If it is a shell, you can find V of solid part by subtracting inner empty sphere from total..
V of entire sphere \(\frac{4}{3} * pi *(5r)^3\)and V of inner empty space = \(\frac{4}{3} * pi *(2r)^3\)..

so V of solid =\(\frac{4}{3} * pi *(5r)^3 - \frac{4}{3}* pi *(2r)^3........................ = \frac{4}{3}*pi*r^3*(125-8)....................... = \frac{4}{3}pi*r^3*117\)

NOW \(\frac{4}{3}pi*r^3\) weighs 40 pounds,
so \(\frac{4}{3}pi*r^3*117\) will weigh \(40*117 = 4680\)...

E


The way you explained was really good, thanks a lot.
One small question, how did you consider v=w?
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8632
Re: The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere  [#permalink]

Show Tags

New post 23 Jul 2017, 06:36
Buttercup3 wrote:
chetan2u wrote:
srmessi wrote:
Can any1 help me with This


Hi,

the V = \(\frac{4}{3}pi*r^3\) and this volume weighs 40 pounds...

If it is a shell, you can find V of solid part by subtracting inner empty sphere from total..
V of entire sphere \(\frac{4}{3} * pi *(5r)^3\)and V of inner empty space = \(\frac{4}{3} * pi *(2r)^3\)..

so V of solid =\(\frac{4}{3} * pi *(5r)^3 - \frac{4}{3}* pi *(2r)^3........................ = \frac{4}{3}*pi*r^3*(125-8)....................... = \frac{4}{3}pi*r^3*117\)

NOW \(\frac{4}{3}pi*r^3\) weighs 40 pounds,
so \(\frac{4}{3}pi*r^3*117\) will weigh \(40*117 = 4680\)...

E


The way you explained was really good, thanks a lot.
One small question, how did you consider v=w?


Hi..

It is not that the volume and weight is being equalled.
We are finding a relationship between the two as the weight will depend on the volume
Say you have a cake with a weight of 20 pounds and you cut 10 piece. What will be the weight of each piece. Ofcourse 20/10..
Here we are talking of volume and not pieces but finally that entire cake has a certain volume and by making 10 EQUAL parts, we are cutting the volume in 10 parts.
Otherwise volume*density= weight.
_________________
Senior Manager
Senior Manager
avatar
P
Joined: 31 Jul 2017
Posts: 499
Location: Malaysia
Schools: INSEAD Jan '19
GPA: 3.95
WE: Consulting (Energy and Utilities)
The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere  [#permalink]

Show Tags

New post 01 Dec 2017, 08:01
2
srmessi wrote:
Image
The volume of a sphere with radius r is \(\frac {4}{3} \pi r^3\). A solid sphere of radius r that is made of a certain material weighs 40 pounds. The figure above shows half of a spherical shell made of the same material. What is the weight, in pounds, of the entire spherical shell if the outer radius is 5r and the inner radius is 2r?

A. 120
B. 360
C. 840
D. 1,080
E. 4,680

Attachment:
Untitled.png
Attachment:
GmatPrepImage.png


Hi,

We can use the Density = Mass/Volume Formula. From the Statement Density = 40/\(\frac {4}{3} \pi r^3\)
As the above figure is made up of same material Density will be same. So,

40/\(\frac {4}{3} \pi r^3\) = x/\(\frac {4}{3} \pi (5r)^3\) - \(\frac {4}{3} \pi (2r)^3\)

x = 4680.
Manager
Manager
avatar
B
Joined: 10 Sep 2014
Posts: 73
Location: Bangladesh
GPA: 3.5
WE: Project Management (Manufacturing)
Re: The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere  [#permalink]

Show Tags

New post 05 Apr 2018, 21:22
VeritasPrepKarishma , Bunuel I'm not getting the concept of this problem. Could you please explain this problem with a simple approach? Thanks.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64317
The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere  [#permalink]

Show Tags

New post 06 Apr 2018, 01:35
4
sadikabid27 wrote:
VeritasPrepKarishma , Bunuel I'm not getting the concept of this problem. Could you please explain this problem with a simple approach? Thanks.


Image
The volume of a sphere with radius r is \(\frac {4}{3} \pi r^3\). A solid sphere of radius r that is made of a certain material weighs 40 pounds. The figure above shows half of a spherical shell made of the same material. What is the weight, in pounds, of the entire spherical shell if the outer radius is 5r and the inner radius is 2r?

A. 120
B. 360
C. 840
D. 1,080
E. 4,680

We have a sphere with radius of 5r with spherical empty space inside with radius of 2r.

The volume of a sphere with radius 5r is \(\frac {4}{3} \pi (5r)^3=125(\frac {4}{3} \pi r^3)\).

The volume of a sphere with radius 2r is \(\frac {4}{3} \pi (2r)^3=8(\frac {4}{3} \pi r^3)\).

The volume of solid material of the given hollow sphere = the volume of the sphere - the volume of the empty space = \(125(\frac {4}{3} \pi r^3)-8(\frac {4}{3} \pi r^3)=117(\frac {4}{3} \pi r^3)\).

Since solid sphere of radius r having the volume of \(\frac {4}{3} \pi r^3\), that is made of a certain material weighs 40 pounds, then our hollow sphere made of the same material and having the volume of \(117(\frac {4}{3} \pi r^3)\), will weigh \(117*40=4,680\).

Answer: E.

Hope it's clear.
_________________
Manager
Manager
avatar
B
Joined: 10 Sep 2014
Posts: 73
Location: Bangladesh
GPA: 3.5
WE: Project Management (Manufacturing)
Re: The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere  [#permalink]

Show Tags

New post 06 Apr 2018, 02:15
Bunuel For the volume of the sphere why are we taking "outer radius 5r" and "inner radius 2r" for the volume of the empty space? I can't identify it from the pic which one is the inner or outer radius, which one is solid sphere and spherical shell. Please explain these to me. Thanks.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64317
Re: The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere  [#permalink]

Show Tags

New post 06 Apr 2018, 02:50
2
sadikabid27 wrote:
Bunuel For the volume of the sphere why are we taking "outer radius 5r" and "inner radius 2r" for the volume of the empty space? I can't identify it from the pic which one is the inner or outer radius, which one is solid sphere and spherical shell. Please explain these to me. Thanks.


We have a sphere with radius of 5r with spherical empty space inside with radius of 2r.

Here is a cross section:

Image

Attachment:
Untitled.png
Untitled.png [ 10.27 KiB | Viewed 31978 times ]

_________________
Manager
Manager
avatar
B
Joined: 16 Jul 2018
Posts: 100
GMAT ToolKit User Premium Member CAT Tests
Re: The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere  [#permalink]

Show Tags

New post 23 Nov 2019, 02:16
Bunuel wrote:
sadikabid27 wrote:
VeritasPrepKarishma , Bunuel I'm not getting the concept of this problem. Could you please explain this problem with a simple approach? Thanks.


Image
The volume of a sphere with radius r is \(\frac {4}{3} \pi r^3\). A solid sphere of radius r that is made of a certain material weighs 40 pounds. The figure above shows half of a spherical shell made of the same material. What is the weight, in pounds, of the entire spherical shell if the outer radius is 5r and the inner radius is 2r?

A. 120
B. 360
C. 840
D. 1,080
E. 4,680

We have a sphere with radius of 5r with spherical empty space inside with radius of 2r.

The volume of a sphere with radius 5r is \(\frac {4}{3} \pi (5r)^3=125(\frac {4}{3} \pi r^3)\).

The volume of a sphere with radius 2r is \(\frac {4}{3} \pi (2r)^3=8(\frac {4}{3} \pi r^3)\).

The volume of solid material of the given hollow sphere = the volume of the sphere - the volume of the empty space = \(125(\frac {4}{3} \pi r^3)-8(\frac {4}{3} \pi r^3)=117(\frac {4}{3} \pi r^3)\).

Since solid sphere of radius r having the volume of \(\frac {4}{3} \pi r^3\), that is made of a certain material weighs 40 pounds, then our hollow sphere made of the same material and having the volume of \(117(\frac {4}{3} \pi r^3)\), will weigh \(117*40=4,680\).

Answer: E.

Hope it's clear.


Hello Bunuel the reason why we realised that there is an empty space inside the sphere is because of the use of word 'shell' ?
Manager
Manager
avatar
B
Joined: 03 Aug 2015
Posts: 82
Location: India
Concentration: Finance, Operations
GMAT 1: 720 Q49 V38
WE: Consulting (Consulting)
The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere  [#permalink]

Show Tags

New post 28 Feb 2020, 05:22
It is a straightforward question, but the visual does not make it clear that the inner sphere is empty especially when the text of the question doesn't make it apparent. I was stuck on it for a while on GMATPrepExam, then assumed that the question is asking for the difference in volume adjusted weight. It is surprising because in PS questions, the stem is generally very clear and without any ambiguity. For example, even in the same question - formula of a sphere is provided. Most of the times, PS questions don't mind giving redundant information through text that is already there in the pic.

Bunuel VeritasKarishma Have you come across other questions for geometry such as these, in which text is silent on a critical information and one has to rely on visual approach?
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 10506
Location: Pune, India
Re: The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere  [#permalink]

Show Tags

New post 01 Mar 2020, 23:55
1
Sparta_750 wrote:
It is a straightforward question, but the visual does not make it clear that the inner sphere is empty especially when the text of the question doesn't make it apparent. I was stuck on it for a while on GMATPrepExam, then assumed that the question is asking for the difference in volume adjusted weight. It is surprising because in PS questions, the stem is generally very clear and without any ambiguity. For example, even in the same question - formula of a sphere is provided. Most of the times, PS questions don't mind giving redundant information through text that is already there in the pic.

Bunuel VeritasKarishma Have you come across other questions for geometry such as these, in which text is silent on a critical information and one has to rely on visual approach?



The question says that it is a spherical shell. It means it is hollow inside. A sphere is the one which is solid.
Also the question mentions outer and inner radii. So that is a hint that it is hollow inside. This is a GMAT prep question so it means you are expected to know what a spherical shell is. The diagram doesn't tell us much.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT Club Bot
Re: The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere   [#permalink] 01 Mar 2020, 23:55

The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne