deriving expression help
Derive an expression that gives the density p of the sphere in terms of its mass m and diameter d .
density = volume of sphere
I cant just substitute in v into the density formula, as I need to have it in diameter instead of radius, been trying for sometime now, how do I get diameter into the formula?
any help appreciated.
1. You are supposed to know that a diameter is twice as long as a radius:
Originally Posted by Tweety
2. The volume becomes:
3. ... and now it's your turn.
The radius is equal to half of the diameter.
Therefor r = d/2.
r^3 = (d/2)^3
r^3 = d^3 / 8
so the volume of the cylinder is equal to (pi * d^3) / 6
which leads to that p = m / ((pi * d^3) / 6 )
rearrange it and u derive to that the density is equal to 6m / (pi * d^3)
thanks guys, I thought d = r^2, so thats why I was stuck.
I also need help on the second part, ;
from this derive an expression that gives the resolution of the density measurement in terms of the resolution of the mass and diameter measurements and respectively.
my booklet gives me this equation for resolution
I am not even sure what exactly is being asked here, but I did manage to work out
density = and from the rearranged volume formula
so if I jut plug in v into density formula, than differentiate I get
If this is correct, than can someone please help me with the other part of the equation, deltap/deltaaV