PanMaths.comFree Printable Math Formula Reference Sheet
Volume of a Rectangular Prism & Cube
Geometry โข Grades 5, 6, 7, 8
Geometry
Volume of a Rectangular Prism & Cube
Calculate the 3D volume (V = lwh) and surface area of a box, cuboid, or cube.
The Formula
V = l ร w ร 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
โกLive Interactive Quick Solver
Instant CalculationPrism Volume (V):240 unitsยณ
Surface Area: 248 unitsยฒโข Step: V = 6 ร 4 ร 10 = 240
V = l \cdot w \cdot h, \quad A = 2(lw + lh + wh)
PDF + Answer Keysโญ Master PDF Workbook$3.99
The Ultimate Math Formula Handbook (36-Page Master Edition)
- โ50 curated printable worksheets in 1 PDF
- โ100% verified step-by-step answer keys
- โUnlimited classroom & homeschool print license
๐ Instant PDF Download โข Secure Checkout via Gumroad & PayPal
๐ฏ Key Concepts & Rules
Essential principles for calculating with this formula:
๐ฆ
V = Length ร Width ร HeightMultiply all 3 dimensions to find volume.
๐ง
Cube: V = sยณWhen all sides are equal, volume is side length cubed.
๐
Surface Area: 2(lw + lh + wh)Sum of the areas of all 6 rectangular faces.
๐ Worked Examples & Step-by-Step Solutions
Example 1: Box Dimensions 8 ร 5 ร 3 cm
Problem:
Find volume and surface area for length 8 cm, width 5 cm, height 3 cm.1
Volume
V = 8 ร 5 ร 3 = 120 cmยณ2
Surface Area
A = 2(8ร5 + 8ร3 + 5ร3) = 2(40 + 24 + 15) = 2(79) = 158 cmยฒAnswer: V = 120 cmยณ, A = 158 cmยฒ
๐ก Pro Tips & Common Mistakes
Space Diagonal
Longest internal corner-to-corner diagonal = โ(lยฒ + wยฒ + hยฒ).
Advertisement