Answer :
Final answer:
The unknown metal cube with a mass of 51.7 mg and a 1.61 mm side has a density of approximately 12.43 g/cm³ after conversion and calculation. Lead has a known density closest to this value, making it the most likely identity of the metal (option c).
Explanation:
To determine the identity of the metal for the cube with a mass of 51.7 mg and a side length of 1.61 mm, we need to calculate its density.
First, we convert the given mass from milligrams to grams and the side length from millimeters to centimeters:
Mass = 51.7 mg = 0.0517 g
Side length = 1.61 mm = 0.161 cm
Next, we calculate the volume of the cube:
Volume = (side length)^3 = (0.161 cm)^3 = 0.004161 cm³
Then, we find the density by dividing the mass by the volume:
Density = mass / volume = 0.0517 g / 0.004161 cm³ = 12.43 g/cm³ (approximately)
Comparing this density with the known densities of the metals listed, lead has a density closest to our calculation (11.3 g/cm³). Therefore, lead is the most likely identity of the unknown metal.
