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for a spherical object what is its mass in terms of the density of the material, its diameter and any necessary constants?

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well volume of a sphere is \[\frac 43 \pi r^3\]
and then density = mass/volume
\[\rho=\frac mV\] \[m=V\rho\]

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Other answers:

so you have \[m = \frac 43\rho \pi r^3\]
where \(\rho\) = density
what about its diameter
change r to d/2
and \(r\) is the radius (half the diameter) \(r=\frac d2\)
radius = diameter/2 so just change r to d/2
ok so thats the final solution?
replace r with d/2....
ok cool and can i give you guys both metals or does just one of you get it?
hey so its (4/3)p(pi)(d/2)^3
is that right?
you can simplify the numbers a bit won't let me give you a metal now
why cant i give it to both of you
i dont mind about that
\[m=\frac43\rho\pi\left(\frac d2\right)^3\] use \[\left(\frac{a}{b}\right)^n=\frac {a^n} {b^n}\]
so it simplifies to 4p(pi)(d/2)?
i crossed out the 3's
what he meant was distribute the exponent
you can not cancel an index with denominator like that
oh so whats it turn to?
\[\left(\frac{a}{b}\right)^n=\frac {a^n} {b^n}\] \[\left(\frac{d}{2}\right)^3=\frac {d^3} {2^3}\]
thanks :)
can you simplify the numbers in the equation now?
yes (4/3)p(pi)(d^3/8) ?
you can simplify it further
you can multiply the denominators
so 4p(pi)(d/8) ? ?
what happened?
can you simplify it?
you canceled the denominaotr and teh exponent???
it can't be simplified?
it just simplified it wrong....multiply the denominators
don't touch anything else
so it (4/24)p(pi)(d^3) ?
thats better!
yes. now express 4/24 in lowest terms
ok so 1/6 p(pi)(d^3) ? thats final!!!!
your turn @UnkleRhaukus
so the constants necessary to express the volume in terms of diameter are ; the natural number; 6 the density of the material rho; \(\rho\) the geometrical constant pi; \(\pi\) the diameter of the sphere \(d\) and the dimensional constant \(3\)

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