Error propagation: it's tricky to measure the diameter of a cylinder without calipers, but a student proposes to do it by using a ruler to measure the length, weighing it, and knowing what the density

Error propagation: it's tricky to measure the diameter of a cylinder without calipers, but a student proposes to do it by using a ruler to measure the length, weighing it, and knowing what the density of the material is. if we know both the mass and density to a precision of 1%, how accurately do we need to measure the length to get the diameter to a precision of 1% as well?