Question

The sides of a small rectangular box are measured to be 1.80±0.01cm, 2.05±0.02cm, and 3.1±0.1 cm long. Calculate its volume and uncertainty in cubic centimeters.

Answer 1

Answer:

The volume of the rectangular box and its uncertainty in cubic centimeters is:

11.44±0.54 $cm^3$

Step-by-step explanation:

We know the volume of a rectangular box is the multiplication of the sides:

$Volume= 1.80cm*2.05cm*3.10cm\\Volume=11.44cm^3$

Now we need to know the uncertainty, the uncertainty of a multiplication is:

$\frac{δ_v}{|Volume|}=\frac{δ_S_1}{|S_1|}+ \frac{δ_S_2}{|S_2|}+\frac{δ_S_3}{|S_3|}$ (1)

Where:

$δ_v$: Volume uncertainty

$δ_S_1$: Side 1 uncertainty (0.01cm)

$δ_S_2$: Side 2 uncertainty (0.02cm)

$δ_S_3$: Side 3 uncertainty (0.10cm)

$S_1$: Side 1 (1.80cm)

$S_2$: Side 2 (2.05cm)

$S_3$: Side 3 (3.10cm)

Clearing the uncertainty of the volume:

${δ_v}=(\frac{δ_S_1}{|S_1|}+ \frac{δ_S_2}{|S_2|}+\frac{δ_S_3}{|S_3|})*Volume$ (2)

${δ_v}=(\frac{0.01}{|1.80|}+ \frac{0.02}{|2.05|}+\frac{0.10}{|3.10|})*11.44cm^3$

$δ_v=0.54cm^3$

The volume of the rectangular box and its uncertainty in cubic centimeters is:

11.44±0.54 $cm^3$