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Difficulty: MediumProperties of Matter

A solid rectangular block of an unknown metal has dimensions of 5 cm5\text{ cm} in length, 4 cm4\text{ cm} in width, and 2 cm2\text{ cm} in height. If the total mass of the block is 316 g316\text{ g}, what is the density of the metal in g/cm3\text{g/cm}^3?

Answer: 7.9 g/cm^3

Answer

The density of the metal block is 7.9 g/cm37.9\text{ g/cm}^3.
Density measures mass per unit volume (D=mVD = \frac{m}{V}). The volume of the rectangular prism is calculated by multiplying its dimensions (5 cm×4 cm×2 cm=40 cm35\text{ cm} \times 4\text{ cm} \times 2\text{ cm} = 40\text{ cm}^3). Dividing the mass (316 g316\text{ g}) by this volume (40 cm340\text{ cm}^3) yields 7.9 g/cm37.9\text{ g/cm}^3.

Step-by-Step Solution

1
Calculate the volume of the rectangular metal block from its dimensions.
V=5 cm×4 cm×2 cm=40 cm3V = 5\text{ cm} \times 4\text{ cm} \times 2\text{ cm} = 40\text{ cm}^3
To determine density, the total volume must first be calculated from the given geometric measurements.
2
Divide the mass of the block by its calculated volume.
Density=316 g40 cm3=7.9 g/cm3\text{Density} = \frac{316\text{ g}}{40\text{ cm}^3} = 7.9\text{ g/cm}^3
Density is defined as mass per unit volume (D=mVD = \frac{m}{V}).

Key Concept

Density is a characteristic physical property of matter defined as mass divided by volume (D=mVD = \frac{m}{V}).
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Topics

Properties of Matter

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