What Is The Volume Of An Object Whose Density E Is 10g/cm³, And A Mass Of 1.50 Kg

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Understanding Density and Mass

Density is a fundamental concept in physics that describes the amount of mass per unit volume of a substance. It is typically denoted by the symbol ρ (rho) and is measured in units of mass per unit volume, such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). On the other hand, mass is a measure of the amount of matter in an object and is typically denoted by the symbol m. In this article, we will explore how to calculate the volume of an object given its density and mass.

The Formula for Density

The formula for density is:

ρ = m / V

where ρ is the density, m is the mass, and V is the volume. Rearranging this formula to solve for volume, we get:

V = m / ρ

Given Values

We are given that the density of the object is 10 g/cm³ and its mass is 1.50 kg. We need to convert the mass from kilograms to grams, as the density is given in g/cm³.

1.50 kg = 1500 g

Converting Units

To ensure that our units are consistent, we need to convert the density from g/cm³ to kg/m³. We know that 1 kg = 1000 g and 1 m³ = 1000 cm³, so:

10 g/cm³ = 10 kg/m³ (since 1 kg = 1000 g and 1 m³ = 1000 cm³)

Calculating the Volume

Now that we have the mass in grams and the density in kg/m³, we can plug these values into the formula for volume:

V = m / ρ = 1500 g / 10 kg/m³ = 150 m³

However, we need to convert the volume from cubic meters to cubic centimeters, as the density is given in g/cm³. We know that 1 m³ = 1000 cm³, so:

150 m³ = 150,000 cm³

Conclusion

In this article, we have shown how to calculate the volume of an object given its density and mass. We used the formula V = m / ρ and plugged in the given values to find the volume. We also converted the units to ensure that they were consistent. The final answer is 150,000 cm³.

Example Problems

  1. An object has a density of 20 g/cm³ and a mass of 2.50 kg. What is its volume?
  2. A block of wood has a density of 0.50 g/cm³ and a mass of 500 g. What is its volume?
  3. A metal rod has a density of 10 kg/m³ and a mass of 5.00 kg. What is its volume?

Solutions

  1. V = m / ρ = 2.50 kg / 20 g/cm³ = 125 cm³
  2. V = m / ρ = 500 g / 0.50 g/cm³ = 1000 cm³
  3. V = m / ρ = 5.00 kg / 10 kg/m³ = 0.5 m³ = 500,000 cm³

Key Takeaways

  • Density is a measure of the amount of mass per unit volume of a substance.
  • The formula for density is ρ = m / V.
  • To calculate the volume of an object given its density and mass, we can use the formula V = m / ρ.
  • We need to ensure that our units are consistent when calculating the volume.
  • We can convert units by using conversion factors, such as 1 kg = 1000 g and 1 m³ = 1000 cm³.