Volume of Rectangular Prism - Definition, Examples, Quiz, FAQ, Trivia
Learn to calculate the space inside rectangular objects with easy explanations and practice activities
What is Volume of a Rectangular Prism?
Volume tells us how much space is inside a 3-dimensional shape. For a rectangular prism (also called a rectangular box or cuboid), volume measures how much the shape can hold.
Think of a rectangular prism as a box with six rectangular faces. It has three dimensions: length, width, and height.
We measure volume in cubic units like cubic centimeters (cm³) or cubic inches (in³). One cubic centimeter is the space taken by a cube that's 1 cm long, 1 cm wide, and 1 cm high.
Understanding volume helps us solve real-world problems like:
- How much water fits in a fish tank
- How many books fit on a bookshelf
- How much soil is needed to fill a garden bed
Key Concept
Volume measures the space inside a 3D shape. For rectangular prisms, volume = length × width × height.
How to Calculate Volume
Calculating the volume of a rectangular prism is simple once you know the formula:
Volume Formula
Where:
V = Volume
l = Length
w = Width
h = Height
Alternative Formula
Where:
B = Base Area (length × width)
h = Height
Example: Find the volume of a rectangular prism that is 8 cm long, 5 cm wide, and 3 cm high.
Step 1: Identify the dimensions → l = 8 cm, w = 5 cm, h = 3 cm
Step 2: Multiply length × width × height → 8 × 5 × 3
Step 3: Calculate the result → 120 cubic centimeters (cm³)
So the volume is 120 cm³. That means 120 cubes of 1 cm³ each would fit inside this prism.
Remember
Always include the units in your answer (like cm³ or m³). Volume is measured in cubic units!
Real-World Examples
Let's practice volume calculation with some real-world examples:
Example 1: Cereal Box
Length: 20 cm
Width: 8 cm
Height: 30 cm
Volume = 20 × 8 × 30 = 4,800 cm³
Example 2: Fish Tank
Length: 60 cm
Width: 30 cm
Height: 40 cm
Volume = 60 × 30 × 40 = 72,000 cm³
(That's 72 liters of water!)
Example 3: Classroom
Length: 10 m
Width: 8 m
Height: 3 m
Volume = 10 × 8 × 3 = 240 m³
Example 4: Pencil Case
Length: 18 cm
Width: 6 cm
Height: 4 cm
Volume = 18 × 6 × 4 = 432 cm³
Practice Tip
Look for rectangular prisms around you and estimate their volume. Then measure to check your estimate!
Volume Practice Quiz
Test your volume calculation skills with this 5-question quiz. Choose the correct answer for each question.
Frequently Asked Questions
Here are answers to common questions about volume of rectangular prisms:
Volume Trivia
Discover interesting facts about volume and measurement:
Ancient Volume Measurement
The ancient Egyptians were among the first to develop volume measurement systems around 3000 BC. They used volume to measure grain harvests and calculate taxes using special units called "hekat."
World's Largest Prism
The world's largest rectangular prism is the Great Wall of China storage facility, measuring 360m long, 120m wide, and 15m high. Its volume is approximately 648,000 cubic meters!
Water Volume
Earth's oceans contain about 1.332 billion cubic kilometers of water. If this water formed a cube, each side would be about 1,100 kilometers long - roughly the distance from New York to Florida!
Smallest Volume Measurement
Scientists can measure volumes as small as a cubic yoctometer (ym³). That's 10⁻⁷² cubic meters - so small that a single proton has a volume of about 10⁻⁴⁵ ym³!
