What is the density (g/mL) of each of the following samples?
a. An ebony carving has a mass of 275 g and a volume of 207 cm³.

Verified step by step guidance

1. Step 1: Recall the formula for density, which is \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). This formula relates the mass of a substance to its volume.
2. Step 2: Identify the given values in the problem. The mass of the ebony carving is \( 275 \; \text{g} \), and the volume is \( 207 \; \text{cm}^3 \).
3. Step 3: Ensure the units are compatible. In this case, grams (g) for mass and cubic centimeters (cm³) for volume are appropriate because \( 1 \; \text{cm}^3 \) is equivalent to \( 1 \; \text{mL} \).
4. Step 4: Substitute the given values into the density formula: \( \text{Density} = \frac{275 \; \text{g}}{207 \; \text{cm}^3} \).
5. Step 5: Perform the division to calculate the density. The result will be expressed in \( \text{g/mL} \), as \( \text{cm}^3 \) is equivalent to \( \text{mL} \).

Key Concepts

Density

Density is a physical property defined as the mass of a substance divided by its volume. It is typically expressed in grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³). Understanding density is crucial for determining how much matter is contained in a given volume, which can help identify materials and their properties.

Mass

Mass is a measure of the amount of matter in an object, usually measured in grams (g) or kilograms (kg). In the context of the question, the mass of the ebony carving is given as 275 g. Mass is a fundamental property that, along with volume, is used to calculate density.

Volume

Volume is the amount of space that a substance occupies, commonly measured in cubic centimeters (cm³) or liters (L). In this question, the volume of the ebony carving is provided as 207 cm³. Knowing the volume is essential for calculating density, as it is the denominator in the density formula.