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705-805 (Hard)|   Geometry|      
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Bunuel
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If the same amount of material is used to make a hollow cylinder and a 17 Sep 2018, 22:05
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85% (hard)

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43% (02:20) correct 57% (02:24) wrong based on 99 sessions

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If the same amount of material is used to make a hollow cylinder and a hollow cube, which one of the two will have a greater height?

(1) The perimeter of the base of the cube is larger than the circumference of the base of the cylinder.
(2) The volume enclosed by the cylinder is 30π.
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E
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If the same amount of material is used to make a hollow cylinder and a 26 Sep 2018, 21:12
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given : a^3 = pi*r^2*h or (a^3/pi*h)^1/2 = r. Asked = To comment on ratio of a/h

statement 1 Sufficient. -----4a>2pi*r ----- After deuducing, --- h/a > Pi*4
Statement 2 Insufficient.


Where have i gone wrong :)
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If the same amount of material is used to make a hollow cylinder and a 27 Sep 2018, 21:41
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chetan2u

Hi !!! your two cents on this one sir :)

Regards
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If the same amount of material is used to make a hollow cylinder and a 27 Sep 2018, 23:07
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Bunuel
If the same amount of material is used to make a hollow cylinder and a hollow cube, which one of the two will have a greater height?

(1) The perimeter of the base of the cube is larger than the circumference of the base of the cylinder.
(2) The volume enclosed by the cylinder is 30π.
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Hi..

Shank18, you have gone wrong in assuming that material means volume..
Yes, it would be correct of the elements were solid, here they are hollow..

So volume of material use will equal to SURFACE AREA*THICKNESS of each item..
So \(t_1*2πrh=t_2*6l^2\)
We have to find l:h


(1) The perimeter of the base of the cube is larger than the circumference of the base of the cylinder.
\(4l>2πr.....2l>πr\)
Insufficient

(2) The volume enclosed by the cylinder is 30π
\(πr^2h=30π......r^2h=30\)
Not sufficient information given

Combined..
We do not the ratio of \(t_1\) and \(t_2\), the thickness of each..
Insufficient

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If the same amount of material is used to make a hollow cylinder and a 27 Sep 2018, 23:57
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Agree with the explanation. But, shouldn't the thickness be negligible to consider since it's hollow ?


Btw sir , you have explained this wonderfully well...Thanks :)

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If the same amount of material is used to make a hollow cylinder and a 29 Sep 2018, 11:37
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chetan2u
hello, could you please explain why you took (2 pi r h) = surface area of the budy of cylinder with out the two bases?
and why you took (6 l^2) not (4 L *6) ?
thanks
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If the same amount of material is used to make a hollow cylinder and a 29 Sep 2018, 20:41
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Qusay
chetan2u
hello, could you please explain why you took (2 pi r h) = surface area of the budy of cylinder with out the two bases?
and why you took (6 l^2) not (4 L *6) ?
thanks
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Hi..
It is not given if base and top are there, so you could take that also, but the main point is that there is nothing about thickness, so you can't find the answer..
Surface area of cube will be (6 faces*areaa of each face)=(6*L^2)

Shank18,
Hollow just means it is not solid but you cannot take the thickness to be 0..
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If the same amount of material is used to make a hollow cylinder and a 29 Sep 2018, 23:09
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Hi Chetan2u,
Shouldn't the statement 1 be--4l>2πr(since perimeter of base of cube will be 4l) and not

(1) The perimeter of the base of the cube is larger than the circumference of the base of the cylinder.
2l>2πr.....l>πr
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If the same amount of material is used to make a hollow cylinder and a 30 Sep 2018, 00:10
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dvishal387
Hi Chetan2u,
Shouldn't the statement 1 be--4l>2πr(since perimeter of base of cube will be 4l) and not

(1) The perimeter of the base of the cube is larger than the circumference of the base of the cylinder.
2l>2πr.....l>πr
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dvishal387,
Yes you are correct. I was not interested in other values as not knowing thickness was not helping us
Thanks
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