The density of a solid cube is determined by measuring its mass and its edge length. The measured mass is M = (40.0 0.4) kg and the measured edge length is l = 2.0 m. If the maximum percentage error in the calculated density is 7 % , what is the absolute error in the measurement of the edge length?

Step-by-step solution

The density of a cube is given by = M l^3 . The maximum percentage error in density is given by: 100 = ( M M 100 ) + 3 ( l l 100 ) First, calculate the percentage error in mass: % M = 0.4 40.0 100 = 1 % Substitute the known values into the error equation: 7 % = 1 % + 3( % l) 3( % l) = 6 % % l = 2 % The percentage error in the edge length is 2 % . To find the absolute error l : l l 100 = 2 l 2.0 100 = 2 l = 4.0 100 = 0.04 m Answer: 0.04 m