Question

If the percentage error in the side of cube is 3/0then the percentage error in the value of cube

Answer 1

Explanation:

If the percentage error in the side is a cube is 3%, what is the percentage error in its volume?

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The volume of a cube is given as

[math]A=s^3[/math]

where [math]s[/math] is the length of one side

Taking the derivative and rearranging

[math]\frac{dA}{ds}=3s^2 \\ dA=3s^2ds[/math]

Since the change in the length of the side is 3% of the side, the change can be written as [math]0.03s[/math]

Substituting this in

[math]dA=3s^2\left(0.03s\right) \\ dA=0.09s^3[/math]

Therefore, the “percentage error” of the volume is 9%