In an experiment to measure the density of the material of a sphere, an error of 2 % occurred while measuring the radius of a sphere and an error of 3 % occurred while measuring the mass of the sphere. What is the maximum percentage error in the measurement of density?

Step-by-step solution

The density of a sphere is given by the formula = M V , where M is the mass and V is the volume. The volume of a sphere is V = 4 3 r^3 , where r is the radius. Substituting the expression for volume into the density formula, we get = M 4 3 r^3 = 3M 4 r^3 . The relative error in density is given by = M M + 3 r r . Given that the percentage error in mass M M 100 = 3 % and the percentage error in radius r r 100 = 2 % . The maximum percentage error in density is 100 = ( M M 100 ) + 3 ( r r 100 ) . Substituting the give