The volume of a cuboid helps us measure how much three-dimensional space is enclosed inside any box-shaped object. From water tanks and classrooms to storage boxes and shipping cartons, this formula tells us how much a cuboid can hold. It plays an important role in mathematics, mensuration, construction, packaging, and competitive exams.
Formula for Calculating the Volume of a Cuboid – Overview
| Formula | Variables & Meaning | When It Is Used |
|---|---|---|
| Volume = l × b × h | l = length, b = breadth, h = height | Used to measure how much space a cuboid occupies |
What is the Volume of a Cuboid in Maths?
The volume of a cuboid represents the total amount of three-dimensional space enclosed within its structure. It shows how much material, liquid, or object can fit inside. The volume is always written in cubic units like cm³, m³, or mm³.
A cuboid has six rectangular faces and three main dimensions: length, breadth, and height. To calculate the volume, multiply all three:
Volume = l × b × h
This gives the complete internal capacity of the cuboid.
If the cuboid is a water tank, the formula helps determine how much water it can store. This calculation is commonly used in exams such as CUET, SSC, Banking, and JEE, and in practical scenarios like determining the space inside rooms, parcels, tanks, or rectangular containers.
Examples to Calculate the Volume of a Cuboid
Example 1: l = 6 cm, b = 4 cm, h = 3 cm
Step 1: Volume = l × b × h
Step 2: = 6 × 4 × 3
Step 3: = 72
Answer: The volume of the cuboid is 72 cm³.
Example 2: l = 10 m, b = 5 m, h = 4 m
Step 1: Volume = l × b × h
Step 2: = 10 × 5 × 4
Step 3: = 200
Answer: The volume of the cuboid is 200 m³.
FAQs about the Volume of a Cuboid Formula
Q1. What is the volume of a cuboid?
It is the total three-dimensional space enclosed within the cuboid.
Q2. What is the unit of volume?
Volume is always measured in cubic units such as cm³, m³, or mm³.
Q3. Can a cube and a cuboid have the same volume?
Yes, if the product of their dimensions results in the same value.
Q4. How is a cuboid different from a cube?
A cube has all sides equal, while a cuboid has different length, breadth, and height.
Q5. Where is this formula used in real life?
It’s used for calculating the capacity of rooms, tanks, boxes, containers, and storage units.
Q6. Is the volume always positive?
Yes, because length, breadth, and height cannot be negative.