anonymous
  • anonymous
for a spherical object what is its mass in terms of the density of the material, its diameter and any necessary constants?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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lgbasallote
  • lgbasallote
well volume of a sphere is \[\frac 43 \pi r^3\]
lgbasallote
  • lgbasallote
and then density = mass/volume
UnkleRhaukus
  • UnkleRhaukus
\[\rho=\frac mV\] \[m=V\rho\]

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More answers

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