Volume and Density

Volume is the amount of space an object occupies, while density measures how much mass is contained in a given volume. The relationship between mass, volume, and density is expressed by the formula:

$$Density = \frac{Mass}{Volume}$$

To find the volume of common shapes:

• Cube: Volume = $s^{3}$, where $s$ is the length of a side.
• Rectangular Prism: Volume = $l \times w \times h$, where $l$ is length, $w$ is width, and $h$ is height.
• Cylinder: Volume = $\pi r^{2} h$, where $r$ is the radius and $h$ is the height.
• Sphere: Volume = $\frac{4}{3} \pi r^{3}$, where $r$ is the radius.

Worked Example

Problem: Find the density of a cube with a side length of 3 cm and a mass of 54 g.

1. Calculate the volume of the cube: $$Volume = s^{3} = 3^{3} = 27 \text{ cm}^{3}$$
2. Use the density formula: $$Density = \frac{Mass}{Volume} = \frac{54 \text{ g}}{27 \text{ cm}^{3}}$$
3. Simplify: $$Density = 2 \text{ g/cm}^{3}$$

Thus, the density of the cube is $2 \text{ g/cm}^{3}$.

Key Questions

• What is the volume of a cylinder with a radius of 2 cm and a height of 5 cm?
• If a rectangular prism has dimensions 4 cm, 3 cm, and 2 cm, what is its volume?
• How would you find the mass of an object if its volume is 10 cm³ and its density is 5 g/cm³?
• Calculate the volume of a sphere with a radius of 1 cm.
• A cube has a volume of 64 cm³. What is the length of one side?

Keywords

• Volume
• Density
• Mass
• Cube
• Cylinder