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well volume of a sphere is \[\frac 43 \pi r^3\]

and then density = mass/volume

\[\rho=\frac mV\]
\[m=V\rho\]

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

right

is that right?

you can simplify the numbers a bit

unkle...it 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 can...you 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!!!!

right!!

your turn @UnkleRhaukus

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