Final answer:
The density of the irregularly shaped piece of gold is calculated by dividing its mass (27 g) by the volume of water displaced (3 ml), resulting in a density of 9 g/ml, which is not matched by the given options.
Step-by-step explanation:
The density of an irregularly shaped piece of gold based on its mass and the volume of water it displaces. Density is defined as the mass-to-volume ratio of a substance. In this case, the mass of the gold is 27 g and the increase in water level from 17 ml to 20 ml indicates the volume of the gold is 3 ml (20 ml - 17 ml). Therefore, the density (d) of this gold piece is calculated using the formula d = mass/volume, which yields d = 27 g / 3 ml = 9 g/ml. This result is not one of the options provided, so there might be a mistake in the options given in the question.
The examples provided show how to calculate the density of various substances and how that density can be used to determine volumes or masses in different situations, such as the density of gold (19.3 g/cm³) and how to calculate the volume or mass of different materials based on their densities.