A student measures the mass and radius of a solid sphere to calculate its density. If the percentage errors in the measurement of mass and radius are 2 % and 1.5 % respectively, the maximum percentage error in the calculated density of the sphere will be

Step-by-step solution

The density of a sphere is given by the formula: = M V = M 4 3 R^3 The maximum percentage error in density is given by the sum of the percentage errors of the individual quantities multiplied by their respective powers. Constants like 4 3 do not contribute to the error. 100 = ( M M 100 ) + 3 ( R R 100 ) Given that the percentage error in mass is 2 % and in radius is 1.5 % : 100 = 2 % + 3(1.5 %) 100 = 2 % + 4.5 % = 6.5 % Thus, the maximum percentage error in the calculated density is 6.5 % . Answer: 6.5 %