1. You have a rock with a volume of 15cm² and a mass of 45 g. What is its density?
2. You have a different rock with a volume of 30cm and a mass of 60g. What is its density?
3. A golden-colored cube is handed to you. The person wants you to buy it for 20 K, saying that is a gold nugget. You pull out your old geology text and look up gold in the mineral table, and read that its density is 19.3 g/cm³. You measure the cube and find that it is 2 cm on each side, and weighs 40 g. What is its density? Is it gold? Should you buy it?
1. The density of an object is calculated by dividing its mass by its volume. In this case, the mass of the rock is 45 g, and its volume is 15 cm³. Therefore, the density is 45 g / 15 cm³ = 3 g/cm³.
2. Similarly, the mass of the second rock is 60 g and its volume is 30 cm³. Thus, its density is 60 g / 30 cm³ = 2 g/cm³.
3. To determine the density of the golden-colored cube, divide its mass (40 g) by its volume (2 cm x 2 cm x 2 cm = 8 cm³). Therefore, the density of the cube is 40 g / 8 cm³ = 5 g/cm³.
Comparing the measured density of the cube (5 g/cm³) to the known density of gold (19.3 g/cm³), it is evident that the cube's density does not match that of gold. Therefore, the cube is not made of pure gold.
Whether or not to buy it depends on various factors such as personal preference, sentimental value, or aesthetic appeal. However, if the main reason for purchasing it was its potential value as a gold nugget, it may not be a wise investment.