Calculating Mass of an Iron Cube using Density

Let's find the mass of the iron cube using the given information. We are provided with the side length of the cube and the density of iron. To find the mass, we first need to calculate the volume of the cube.

The given parameters are:

Step-by-Step Solution:

Step 1: Calculate the volume of the cube.

The volume (V) of a cube is calculated by cubing its side length (s). The formula is:

Substitute the given side length into the formula:

\(\qquad V = (2 \text{ cm})^3\)

\(\qquad V = 2 \text{ cm} \times 2 \text{ cm} \times 2 \text{ cm}\)

\(\qquad V = 8 \text{ cm}^3\)

So, the volume of the iron cube is 8 cm³.

Step 2: Calculate the mass of the cube.

The relationship between mass (m), density (\(\rho\)), and volume (V) is given by the formula:

\(\qquad \text{Density} = \frac{\text{Mass}}{\text{Volume}}\)

This can be rearranged to find the mass:

\(\qquad \text{Mass} = \text{Density} \times \text{Volume}\)

Or, using symbols:

\(\qquad m = \rho \times V\)

Substitute the given density and the calculated volume into this formula:

\(\qquad m = 7.8 \text{ gm/cm}^3 \times 8 \text{ cm}^3\)

Now, perform the multiplication:

\(\qquad m = 62.4 \text{ gm}\)

The mass of the iron cube is 62.4 gm.

Let's quickly review the calculation:

• Side = 2 cm
• Volume = \((2 \text{ cm})^3 = 8 \text{ cm}^3\)
• Density = 7.8 gm/cm³
• Mass = Density \(\times\) Volume = 7.8 gm/cm³ \(\times\) 8 cm³ = 62.4 gm

The calculated mass matches one of the options provided.

Revision Table: Key Concepts in Mass, Density, and Volume

Additional Information on Calculating Mass and Density

Understanding the relationship between mass, density, and volume is fundamental in physics and chemistry. Density is an intrinsic property of a substance, meaning it doesn't change regardless of the amount of the substance (as long as temperature and pressure are constant). For example, a small piece of iron has the same density as a large block of iron.

When solving problems involving mass, density, and volume, always ensure that the units are consistent. In this problem, the side was in cm and density in gm/cm³, which allowed direct calculation of volume in cm³ and mass in gm. If units were mixed (e.g., side in meters, density in gm/cm³), you would need to convert them to a consistent system (like all SI units or all CGS units) before calculating.

For objects with irregular shapes, volume can be determined using methods like water displacement, provided the object is denser than the liquid and doesn't react with it.