Use Differentials to find the change in mass?

Question

as a percentage, when the radius r of a solid increases by 2%. Note that the mass of a sphere of uniform density p is given byy.

m = 4/3 ρπ(r^3)

Can anyone do this for me? I cant understand it

Use Differentials to find the change in mass as a percentage, when the radius r of a solid increases by 2%. Note that the mass of a sphere of uniform density p is given by.


m = 4/3 ρπ(r^3)

Can anyone do this for me? I cant understand it

thanks mate, you sound as though you know what your doing.

Appreciate it

Answer 1

first take the derivative of m with respect to r

dm/dr = 4 p*pi*r^2

now divide by the mass m

dm/m = 4p*pi*r^2/(4/3p*pi*r^3) or

dm/m = 3 dr/r

we are given that dr/r (the percent change in r) is 2%

plug that into the last eqn and we get the percent change in mass

dm/m = .06 or 6%