Amount of space occupied by a three dimensional object is called its volume.Every object occupies space. The measurement of this occupied space is the volume of that object. The object may be solid or hollow. In case it is solid, then the space occupied by this solid object is its volume. In case of hollow objects, we know that such object is filled with air or a liquid.So if we are to find the volume of a hollow object, we intend to calculate the space occupied by the air or a liquid in such object. The volume that fills this hollow object is said to be the capacity of the object or container. Therefore, the volume is the space occupied by the object while capacity is the volume of any substance that the object can accommodate inside it.
(i)The Volume of a Cuboid :
For understanding the volume of a cuboid we need to first understand the area of a rectangle since cuboids are a combination of rectangular planes stacked over each other. The height up to which these rectangular planes are stacked helps find the volume of the whole structure.
The area of a rectangle is l×b.
Now since a few rectangular planes are stacked upwards to form a 3d rectangular structure, the volume of the object is Base area × height.
So the volume = space occupied by the cuboid = Base area × height. Volume = A × h. A = l × b. Hence,
Volume of Cuboid (V) = l × b × h
A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?
Find the height of a cuboid of volume 100 cm3, whose length and breadth are 5 cm and 4 cm respectively.
A cuboidal vessel is 10 cm long and 5 cm wide. How high it must be made to hold 300 cm3 of a liquid?