Linearization Word Problem?

**Seigi** · November 18th 2008, 08:20 PM

The edge of a cube is measured as 10 cm with an error of 1%. The cube's volume is to be calculated from this measurement. Estimate the percentage error in the volume calculation.

Please explain to me how to do this.

**TheEmptySet** · November 18th 2008, 08:38 PM

Originally Posted by Seigi

The edge of a cube is measured as 10 cm with an error of 1%. The cube's volume is to be calculated from this measurement. Estimate the percentage error in the volume calculation.

Please explain to me how to do this.

The volume of a cube is

$V=s^3$

The error is $\frac{\Delta V}{V} \approx \frac{dV}{V}$

We know that $s=10cm \mbox{ and } \Delta s =.01(10cm)=0.1cm$

$dV =3s^2ds$

using the above formula we get

$\frac{3(10cm)^2(0.1cm)}{(10cm)^3}=\frac{30cm^3}{10 00cm^3}=\frac{3}{100}=3\%$

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