Question

An interior decorator installs an aquarium that is 0.700 ? wide, 6.00 ? deep, and 9.00 ? long. The uncertainty of each measurement is 0.0200 ?, what is the volume of the aquarium and percent uncertainty in the volume? Significant Figures!

Answer 1

Width of aquarium=w=0.7 m0.02 m

Depth of aquarium=d=6.0 m0.02 m

Length of aquarium=L=9.0 m0.02 m

Volume is given by V=w*d*L

Minimum volume=(0.7-0.02)*(6-0.02)*(9-0.02)=36.516 m³

Maximum volume=(0.7+0.02)*(6+0.02)*(9+0.02)=39.096 m³

Mean value of volume=(36.516+39.096)/2=37.806 m³

Uncertainty=(39.096-37.806)=1.29 m³

Volume of aquarium=37.8061.29 m³

% uncertainty in volume=(1.29/37.806)*100=3.14%