# Thread: Linearization Word Problem need help again

1. ## Linearization Word Problem need help again

A manufacturer contracts to mint coins for the federal government. How much variation dr in the radius of the coins can be tolerated if the coins are to weigh within 1/1000 of their deal weight? Assume the thickness does not vary.
I do not know where to began with this problem, i'm not good at word problem.

2. Originally Posted by Seigi
I do not know where to began with this problem, i'm not good at word problem.
Let r denote the radius of the coin and h its thickness which is considered to be constant.
The weight of the coin is proportional to its volume.

Let dy denote the difference of 2 radii. Then you know that

$\displaystyle \dfrac{dy}{dr}=V'(r)=2\pi\cdot h \cdot r$

The maximum value of $\displaystyle dy=\dfrac1{1000}V$

Therefore:

$\displaystyle 2\pi \cdot h \cdot r \cdot dr=\dfrac1{1000}V = \dfrac1{1000}\cdot \pi\cdot h \cdot r^2$

Solve for dr:

$\displaystyle dr=\dfrac{ \dfrac1{1000}\cdot \pi\cdot h \cdot r^2}{2\pi \cdot h \cdot r} = \dfrac1{2000} r$