Volume of Cubes & Cuboids explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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Volume measures the space inside a solid shape.
Cubes and cuboids are common 3D shapes, so their volume formulas are very useful.
Volume is used for boxes, rooms, tanks, containers, packaging, and storage.
A cuboid has length, breadth, and height. Its volume is found by multiplying these three dimensions.
A cube is a special cuboid with all edges equal.
Volume uses cubic units, such as c and , because it counts unit cubes.
If a larger solid is filled with smaller cubes, divide the larger volume by the smaller cube volume.
Meaning: Volume is the amount of space inside a solid.
Definition: Volume measures threimensional space.
A box that holds more unit cubes has a larger volume.
Meaning: A cuboid volume uses length, breadth, and height.
Definition: Volume of cuboiength x breadth x height.
If lengt cm, breadt cm, and heigh cm, volum x 5 x c.
Meaning: A cube has equal length, breadth, and height.
Definition: Volume of cubide x side x side.
If sid cm, volum x 6 x c.
Meaning: Sometimes one dimension is unknown.
Definition: A missing dimension can be found by dividing volume by the product of the other two dimensions.
If , , and , then .
Meaning: A larger cuboid can be filled with smaller cubes.
Definition: Number of cubeolume of large soliolume of one small cube.
If a large box has volume 1000 c and one small cube has volume 8 c, then 125 cubes fit.
Easy
Question: Find the volume of a cuboid of length 7 cm, breadth 4 cm, and height 5 cm.
Medium
Question: Find the volume of a cube of side 9 cm.
Exam-level
Question: A cuboid has volume 360 c, length 12 cm, and breadth 5 cm. Find its height.
Writing square units for volume
Why it happens: Area units are remembered.
Correct approach: Volume uses cubic units such as c.
Adding dimensions instead of multiplying
Why it happens: Perimeter thinking is used.
Correct approach: Volume of cuboiength x breadth x height.
Using cube formula for cuboid
Why it happens: Both are boike solids.
Correct approach: Use only when all three edges are equal.
Why is volume in cubic units?
Volume counts unit cubes that fill a solid.
Is a cube a cuboid?
Yes. A cube is a special cuboid with all edges equal.
Can volume and capacity be related?
Yes. Capacity is how much a container can hold, and it is linked to volume.
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