Density Mass Volume- Practice Questions and Answers

What You Actually Need to Know About Density, Mass, and Volume

These three concepts show up constantly in physics and chemistry. Most students mix them up at least once. Here's the deal:

• Mass = how much matter is in an object
• Volume = how much space an object takes up
• Density = mass per unit volume

That's it. The math behind them is straightforward. The confusion usually comes from memorizing formulas instead of understanding what you're actually calculating.

The Formulas You Must Know

Three equations. Memorize them.

Volume Formulas for Common Shapes

• Cube: V = s³ (s = side length)
• Rectangular prism: V = l × w × h
• Sphere: V = (4/3)πr³
• Cylinder: V = πr²h

The Density Equation

D = m ÷ V

Where D is density, m is mass, and V is volume. Units matter:

• Density is typically g/cm³ or kg/m³
• Mass is typically grams or kilograms
• Volume is typically cm³, mL, or m³

Density, Mass, and Volume Quick Reference

How to Solve Any Density Problem

Follow these steps in order:

1. Identify what you're given — circle the numbers in the problem
2. Identify what you're solving for — mass, volume, or density
3. Pick the right equation:
   • Solving for density? → D = m ÷ V
   • Solving for mass? → m = D × V
   • Solving for volume? → V = m ÷ D
4. Plug in the numbers
5. Calculate and check your units

Practice Questions

Question 1: Find the Density

A block of aluminum has a mass of 54 g and a volume of 20 cm³. What is the density of the aluminum?

Question 2: Find the Mass

A gold bar has a density of 19.3 g/cm³ and a volume of 15 cm³. What is the mass of the gold bar?

Question 3: Find the Volume

A piece of iron has a mass of 237 g and a density of 7.9 g/cm³. What is the volume of the iron piece?

Question 4: Cube Volume and Density

A metal cube has sides of 3 cm and a mass of 81 g. Calculate the volume and then the density of the cube.

Question 5: Will It Float or Sink?

You have an object with a density of 0.8 g/cm³. Water has a density of 1.0 g/cm³. Will this object float or sink in water?

Question 6: Cylinder Density

A cylindrical rod has a radius of 2 cm and a height of 10 cm. Its mass is 314 g. Calculate the density. (Use π ≈ 3.14)

Answers and Solutions

Answer 1

D = m ÷ V

D = 54 g ÷ 20 cm³

D = 2.7 g/cm³

Answer 2

m = D × V

m = 19.3 g/cm³ × 15 cm³

m = 289.5 g

Answer 3

V = m ÷ D

V = 237 g ÷ 7.9 g/cm³

V = 30 cm³

Answer 4

First find volume:

V = s³ = 3 cm × 3 cm × 3 cm = 27 cm³

Now find density:

D = 81 g ÷ 27 cm³

D = 3.0 g/cm³

Answer 5

The object has a density of 0.8 g/cm³, which is less than water's density of 1.0 g/cm³.

It will float.

Objects with density lower than the fluid they are placed in will float. Objects with higher density will sink.

Answer 6

Step 1: Find the volume of the cylinder

V = πr²h

V = 3.14 × (2 cm)² × 10 cm

V = 3.14 × 4 cm² × 10 cm

V = 125.6 cm³

Step 2: Calculate density

D = m ÷ V

D = 314 g ÷ 125.6 cm³

D = 2.5 g/cm³

Common Mistakes to Avoid

• Mixing up units — Always convert to consistent units before calculating. 1 g/cm³ = 1000 kg/m³
• Forgetting to find volume first — For irregular shapes, use water displacement. For regular shapes, use the geometry formula
• Using the wrong formula — Double-check what you're solving for before you start
• Rounding too early — Keep extra decimal places during calculations, round only at the end

Quick Conversion Reference

These practice questions cover the core scenarios you'll encounter. Work through each one until the process becomes automatic. The formula triangle method helps: cover what you need, and the remaining formula tells you what to do.