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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

16 May 2016, 23:14

2

This post received KUDOS

12

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

64% (01:47) correct 36% (01:32) wrong based on 194 sessions

HideShow timer Statistics

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?

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 \(40*117 = 4680\)...

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?

Re: The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere [#permalink]

Show Tags

17 May 2016, 07:14

srmessi wrote:

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?

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 [ 13.33 KiB | Viewed 8869 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

Re: The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere [#permalink]

Show Tags

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?

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.
_________________

Re: The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere [#permalink]

Show Tags

30 Nov 2017, 23:04

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

How do u know the sphere is hollow? its not mentioned anywhere?

Re: The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere [#permalink]

Show Tags

01 Dec 2017, 07:04

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
_________________

We are more often frightened than hurt; and we suffer more from imagination than from reality

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

Show Tags

01 Dec 2017, 08:01

srmessi wrote:

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?

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,