Question

An object has a mass of 57.6 \(\mathrm{g} .\) Find the object's density, given that its volume is 40.25 \(\mathrm{cm}^{3} .\)

Short answer

The density of the object is 1.431 \(\mathrm{g/cm^{3}}\).

Step-by-step solution

Recall the formula for density

The density (\rho) of an object is given by the formula: \[\rho = \frac{m}{v}\]where \(m\) is the mass and \(v\) is the volume.

Identify the given values

The mass (\(m\)) of the object is 57.6 grams and the volume (\(v\)) is 40.25 cubic centimeters.

Substitute the values into the formula

Substitute the mass and volume into the density formula: \[\rho = \frac{57.6 \, \mathrm{g}}{40.25 \, \mathrm{cm}^{3}}\]

Calculate the density

Perform the division to find the density: \[\rho = \frac{57.6}{40.25} = 1.431 \mathrm{g/cm^{3}}\]

Key concepts

Mass

Mass is a fundamental property of an object. It measures the amount of matter in an object, often perceived as its weight. In the metric system, mass is usually measured in grams (g) or kilograms (kg). It is important to understand mass as it plays a crucial role in finding other physical properties, like density.
To summarize:

• Mass is measured in grams or kilograms.
• It represents the amount of matter in an object.
• It is a crucial variable in the density formula.

Volume

Volume is the amount of space occupied by an object. It is a three-dimensional measurement and is often given in cubic centimeters (cm³) or liters (L). Understanding volume helps us know how big or small an object is and how much space it occupies.
To make it simple:

• Volume is measured in cubic centimeters or liters.
• It tells us how much space an object takes up.
• It is a necessary variable for calculating density.

Density Formula

The density of an object measures how much mass is contained in a given volume. It is a key concept in physics and chemistry, and it helps us understand how dense or compact an object is. The formula for density is given by: