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

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

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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

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[Reveal] Spoiler: OA

Last edited by Bunuel on 17 May 2016, 00:38, edited 2 times in total.
Renamed the topic and edited the question.

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

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New post 16 May 2016, 23:29
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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
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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

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New post 16 May 2016, 23:32
Perfect...
Thanks a lot chetan2u.
Btw is this a 650 level question?

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

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New post 16 May 2016, 23:35
srmessi wrote:
Perfect...
Thanks a lot chetan2u.
Btw is this a 650 level question?


yeah, it should be close to 700 level
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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

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New post 17 May 2016, 00:46
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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

[Reveal] Spoiler:
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Untitled.png
Attachment:
GmatPrepImage.png



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

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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

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

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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?

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

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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.
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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

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New post 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?

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

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

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New post 01 Dec 2017, 08:01
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

[Reveal] Spoiler:
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.

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The volume of a sphere with radius r is (4/3)*pi*r^3. A solid sphere   [#permalink] 01 Dec 2017, 08:01
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