Question

In his travels, Rudolph meets Yukon Cornelius, a prospector looking for silver and gold. Yukon finds a cube, 1-inch on all sides, that has a mass of 0.185 kilograms. What substance is the cube made from?

Answer 1

The density of the 1-inch cube that Yukon Cornelius finds is approximately 11.29 g/cm³, which does not match the densities of common pure elements like silver or gold, indicating it could be made of an alloy or a less common substance.

Step-by-step explanation:

To determine what substance a cube is made from, we need to calculate its density and then compare it to known substance densities. Density is defined as the mass per unit volume. We can calculate the density of the cube Yukon Cornelius finds using the formula:

Density (d) = Mass (m) / Volume (V)

Given that the cube is 1-inch on all sides, its volume in centimeters is (2.54 cm)^3, since 1 inch equals 2.54 centimeters.

Volume (V) = 2.54 cm * 2.54 cm * 2.54 cm = 16.387064 cm³

We must also convert the mass from kilograms to grams for consistency with the volume in cubic centimeters:

Mass (m) = 0.185 kg * 1000 g/kg = 185 g

Now, calculate the density:

Density (d) = 185 g / 16.387064 cm³ ≈ 11.29 g/cm³

This density does not match the density of silver (10.49 g/cm³) or gold (19.32 g/cm³), and is not characteristic of any common pure element, suggesting the cube might be made of an alloy or a less common element.