What is the formula for Volume of a Rectangular Prism & Cube?

The mathematical formula for Volume of a Rectangular Prism & Cube is V = l × w × h. It is used for calculating the 3d volume and surface area of a box, cuboid, or cube.

PanMaths.comFree Printable Math Formula Reference Sheet

Volume of a Rectangular Prism & Cube

Geometry • Grades 5, 6, 7, 8

Geometry

Volume of a Rectangular Prism & Cube

Q: What do the variables in the Volume of a Rectangular Prism & Cube formula represent?

In the formula V = l × w × h: V = Volume (cubic units), l = Length of the base, w = Width of the base, h = Height of the prism.

Q: How do you calculate Volume of a Rectangular Prism & Cube step-by-step?

To calculate volume of a rectangular prism & cube: 1. Identify the given values (V = Volume (cubic units), l = Length of the base, w = Width of the base, h = Height of the prism). 2. Substitute the values into the formula V = l × w × h. 3. Simplify and evaluate step-by-step.

Calculate the 3D volume (V = lwh) and surface area of a box, cuboid, or cube.

The Formula

V = l × w × h

Used for: Calculating the 3D volume and surface area of a box, cuboid, or cube

VVolume (cubic units)

lLength of the base

wWidth of the base

hHeight of the prism

⚡Live Interactive Quick Solver

Instant Calculation

Length (l):

Width (w):

Height (h):

Prism Volume (V):240 units³

Surface Area: 248 units²• Step: V = 6 × 4 × 10 = 240

V = l \cdot w \cdot h, \quad A = 2(lw + lh + wh)

🎮 60s Speed Game→📝 Practice Worksheets→

✨ Free Classroom Assessment ToolSet A & Set B Anti-Cheat

Custom Math Quiz & Test Maker

Need a mixed Friday review or unit assessment? Create a custom test combining multiple math skills in 15 seconds.

✓Anti-cheat Set A & Set B with alternate numbers for adjacent desks
✓100% step-by-step teacher grading keys with intermediate lines
✓1-click Google Classroom links for student tablet/Chromebook testing

✨ Build Custom Worksheet in 15 Seconds →

🎓 100% Free for Teachers & Parents • No Signups Required • Pure Printable PDF

🎯 Key Concepts & Rules

Essential principles for calculating with this formula:

📦V = Length × Width × Height

Multiply all 3 dimensions to find volume.

🧊Cube: V = s³

When all sides are equal, volume is side length cubed.

📐Surface Area: 2(lw + lh + wh)

Sum of the areas of all 6 rectangular faces.

📝 Worked Examples & Step-by-Step Solutions

Example 1: Box Dimensions 8 × 5 × 3 cm

Problem: Find volume and surface area for length 8 cm, width 5 cm, height 3 cm.

VolumeV = 8 × 5 × 3 = 120 cm³

Surface AreaA = 2(8×5 + 8×3 + 5×3) = 2(40 + 24 + 15) = 2(79) = 158 cm²

Answer: V = 120 cm³, A = 158 cm²

💡 Pro Tips & Common Mistakes

Space Diagonal

Longest internal corner-to-corner diagonal = √(l² + w² + h²).

Name: _______________________________Date: _______________Class/Period: _________

Related Formulas

🛢️

GeometryVolume of a Cylinder

→⏢

GeometryArea of a Trapezoid

→🔮

GeometryVolume of a Sphere

→