[Eng.mohammed]

Hi every one , I have some questions about the density  can you help me to solve it ?

1- if you cut the cylinder to two equal parts, what will happen to the density of one part ? and why ?

the solution is : the density is same but I don't know why ?

2- which shape has the highest density , cube , cylinder or sphere ? and why?

the solution is : the sphere but I don't know why ?

can you help me please

[Borek]

What is density in the first place?

[magician4]

in addition:

the allegedly correct answer to # 2 is wrong: "density" is completely independent of the shape of an object

the sphere has the optimum ratio "volume : surface" , yes ...
... but that's not "density"

regards

Ingo

[billnotgatez]

@magician4
it is a poor question but
I thing they imply a homogenous mass (poorly done by the authors of the question)

[curiouscat]

@magician4
it is a poor question but
I thing they imply a homogenous mass (poorly done by the authors of the question)

Even for a homogeneous mass the density of a sphere & cube made of the same material are the same.

I agree with @magician. The answer given in the solution is wrong.

[Tameo]

So if density is Mass/Volume ,what will happen to the mass and volume when the cylinder is cut in half?

[curiouscat]

So if density is Mass/Volume ,what will happen to the mass and volume when the cylinder is cut in half?

Both get halved.

[billnotgatez]

@curiouscat
the question wanted sphere* probably because
From WIKI
The sphere has the smallest surface area of all surfaces that enclose a given volume, and it encloses the largest volume among all closed surfaces with a given surface area.

@Tameo and Eng.mohammed
This problem was supposed* to have you grasp both geometry and density at the same time
plus understand the relationship between them
this is why having a good grasp of mathematics is important for chemistry

*but was poorly worded

[magician4]

one of the most important things pupils have to learn about "density" is , that density is independant of shape of an object for a given homogeneous substance

to state otherwise, esp. as allegedly correct answer to a respective question in context with "density", is not a case of "bad wording" , but plain and simply wrong

... and Socrates would have loved to explain the difference, and why it's important to be crystal clear about this, I think


regards

Ingo

[billnotgatez]

<whimsy on>
Eureka (Archimedes)

or maybe not

if
you know the density
and
you know the shapes and understand volume
then
you can predict the weight

for instance if you want to know the best shape of an airship
with the least surface area to keep cost down
then you know the sphere would be better than a cuboid
but aerodynamics gets in the way
so the next best is a cylinder
of course working more with aerodynamics you can do more trade offs to get the best shape

and yet not all shapes can a volume be easily done (Escher)

I have heard it said
Why should I learn geometry
it is algebra that is essential for chemistry
(Kodachrome Paul Simon [so to speak])

<whimsy off>