To obtain a formula for finding the volume of a cuboid.
Cube and cuboid shapes in Math are three-dimensional shapes. The cube and cuboid are obtained from the rotation of the two-dimensional shapes called square and rectangle respectively.
Cube: A cube is a three-dimensional shape. It has six faces, eight vertices and twelve edges. All the faces of the cube are in square shape and have equal dimensions.
Cuboid: A cuboid is also a polyhedron having six faces, eight vertices and twelve edges. The faces of the cuboid are parallel. But not all the faces of a cuboid are equal in dimensions.
The formula for the volume of the cuboid can be derived from the concept explained on rectangular sheets.
Let the area of a rectangular sheet of paper be 'A', the height up to which they are stacked be 'h' and the volume of the cuboid be 'V'.
Can you tell what would be the relationship between V, A, and h?
The area of the plane region occupied by each rectangle × height = Measure of the space occupied by the cuboid.
So, we get A × h = V
The volume of cuboid = Base area × Height
The base area for cuboid = l × b
Hence, the volume of a cuboid, V = l × b × h = lbh
Let a cuboid of length = 4 units , breadth = 3 units and height = 2 units
Then, by the formula, Volume of the cuboid = (length × breadth × height) cubic units.
So, we get the volume as = 4 x 3 x 2 = 24 cubic units.
Students should already be familiar with
Concept of Area of rectangle:
Let us say a rectangle ABCD of
Then, Area of rectangle ABCD can be defined as = l*b
Concept of Area of square:
Let us say a square ABCD of
Side = x
Then, Area of square ABCD can be defined as= x*x= x²