Homework Help Forum: Calculus

Posted by Salman on Friday, November 6, 2009 at 8:24am.

The circumference of a sphere was measured to be 74 cm with a possible error of 0.5 cm. Use linear approximation to estimate the maximum error in the calculated surface area.

• Calculus - drwls, Friday, November 6, 2009 at 9:40am

  The (small) relative error in a linear dimension, which in this case is 0.676%, gets doubled when you are calculating the relative error in an area dimension. That is the "linear approximation". Here's why: Area = C * r^2 * (1 + e)^2 = C r^2 (1 + 2e + e^2) where e is the relative error in radius (or circumference). For e <<1, you can neglect e^2. 2e becomes the area realtive error. C is a constant. The same rule can be applied to any shape or figure. The relative error in a volume dimension is 3e.

  
  

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