Volume of Cubes and Cuboids – V = s³ and V = lwh
A cube's volume is V = s³ (side cubed), and a cuboid's volume is V = lwh (length × width × height). Both formulas answer the same underlying question: how many 1 × 1 × 1 unit cubes would it take to completely fill the solid? For a cuboid, that's l layers of w × h unit cubes stacked up, giving lwh in total.
A cube is just the special case of a cuboid where l = w = h = s, which is exactly why s³ and s × s × s give the same result – the cube formula is simply the cuboid formula with all three dimensions equal.
Calculating Volume
Cube: V = s³. Cuboid: V = l × w × h. Both count how many unit cubes fill the solid.
Find the volume of a cube with side 5 cm.
V = 5³ = 5 × 5 × 5 = 125 cm³.
Find the volume of a cuboid 8 cm × 5 cm × 3 cm.
V = 8 × 5 × 3 = 120 cm³.
Real-Life Application
- Shipping and storage: calculating how much a box or container can hold.
- Aquariums: finding how much water a rectangular fish tank holds.
- Concrete pouring: calculating the volume of a rectangular concrete slab.
Key Takeaways
- A cube's volume is V = s³; a cuboid's volume is V = lwh.
- Both formulas count how many unit cubes fill the solid.
- A cube is the special case of a cuboid with all three dimensions equal.
Practice: Volume of Cubes and Cuboids
Volume of Cubes and Cuboids
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