Each side of a metal cube is measured to be 2.0 cm ±0.20 cm. What is the absolute uncertainty in the calculated volume of the cube?
the answer is not 4.8
so bad not efficient
To find the absolute uncertainty in the calculated volume of the cube, we need to consider the uncertainty in the side length of the cube.
Given:
Side length of the cube, l = 2.0 cm
Uncertainty in the side length, Δl = 0.20 cm
Absolute uncertainty in the volume can be calculated by taking the derivative of the volume formula with respect to the side length and multiplying it by the uncertainty in the side length.
The volume of a cube is given by V = l³, where l is the side length.
Taking the derivative of V = l³ with respect to l, we get dV/dl = 3l².
Now, multiply the derivative by the uncertainty in the side length to get the absolute uncertainty:
Absolute uncertainty in volume, ΔV = (dV/dl) * Δl
= 3l² * Δl
Substituting the given values:
= 3(2.0 cm)² * 0.20 cm
= 3 * 4 cm² * 0.20 cm
= 2.4 cm³
Therefore, the absolute uncertainty in the calculated volume of the cube is 2.4 cm³.
The relative uncertainty in x^n is n times the relative uncertainty in x.
the relataive uncertainity in the above is 10 percent, so the relative uncertainity in the volume is 30 percent
Volume=8.0+-2.4 cm^3
absolute uncertainity=4.8 cm^3
another way:
high volume-low volume
2.2^3-1.8^3= 4.8cm^3