# Thread: Linearization Word Problem?

1. ## Linearization Word Problem?

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.

2. 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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### if an error of 1% is made inmeasuring the edge of the cube, what is the approximate percentage error comouted in the volume

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