If the same amount of material is used to make a hollow cylinder and a

Question

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.

ShankSouljaBoi · Answer

A
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

ShankSouljaBoi · Answer

chetan2u Hi !!! your two cents on this one sir

Regards

chetan2u · Answer

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

E

ShankSouljaBoi · Answer

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

Posted from my mobile device

Qusay · Answer

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

chetan2u · Answer

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..

dvishal387 · Answer

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

chetan2u · Answer

dvishal387 ,
Yes you are correct. I was not interested in other values as not knowing thickness was not helping us
Thanks

If the same amount of material is used to make a hollow cylinder and a

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