A student calculates the density of a cylindrical wire by measuring its mass, radius, and length. If the student commits a +1.5 % error in the measurement of mass, a -1.0 % error in the measurement of radius, and a +0.5 % error in the measurement of length, the actual percentage error in the calculated value of density is :

Step-by-step solution

The density of a cylinder is given by the formula = M r^2 L Taking the natural logarithm and differentiating, we get the algebraic error relation: = M M - 2 r r - L L The given percentage errors are: M M % = +1.5 % r r % = -1.0 % L L % = +0.5 % Substituting these values into the error equation: % = (+1.5 %) - 2(-1.0 %) - (+0.5 %) % = 1.5 % + 2.0 % - 0.5 % = 3.0 % Answer: 3.0 %