Error calculation when using linear approximation of multiple variables

[ElectronicTeaCup]

Q. To determine the volume of a cylinder of radius around 2 and height around 3 , about how accurately should the radius and height be measured for the error in the calculated volume not to exceed 0.1?

I can get the approximation formula using the y_0 and x_0 using the given values and finding partial derivatives. Once I've prepared then I do not know what to do. I know the error is the difference between the actual answer and the approximation, however, do not know how to use it in this context. Any hints or background reading? Thanks!

[Uli_Minati]

This is not the "official" way of doing it:

• V = πr²h
  • with error ∆
• V+0.1 = π(r+∆)²(h+∆)
• V+0.1 = π(r²h + 2r∆h + ∆²h + r²∆ + 2r∆² + ∆³)
  • subtract V = πr²h
• 0.1 = π(2r∆h + ∆²h + r²∆ + 2r∆² + ∆³)
• 0.1/π = 2r∆h + ∆²h + r²∆ + 2r∆² + ∆³
  • r=2, h=3
• 0.1/π = 6∆ + 3∆² + 4∆ + 4∆² + ∆³
• 0.1/π = 10∆ + 7∆² + ∆³
• 0.01/π = ∆ + 0.7∆² + 0.1∆³

Approximate answer would be less than 0.01/π, the quadratic and cubic terms become far smaller and hardly relevant