Cuboid is a three-dimensional structure having six rectangular faces. These six faces of cuboid exist as a pair of three parallel faces. When the area of the faces of a cuboid is same we call this cuboid as a cube. Area of all the faces of a cube is the same as they are all squares. Now, think of a scenario where we need to calculate the amount of sugar that can be accommodated in a cuboidal box. In other words, we mean to calculate the capacity of this box. The capacity of a cuboidal box is basically equal to the volume of cuboid involved. Thus, the volume of a three-dimensional shape, in general, is equal to the amount of space occupied by that shape. The general formula for the calculation of the volume of a cuboid is given below.
Volume of cuboid: Volume of a cuboid is given by the product of its dimensions.
Volume of cuboid of length ‘l’, breadth ‘b’, height ‘h’ = l×b×h
Volume of cube: Cuboid in which length of each edge is equal is known as a cube. Thus,
Volume of a cube of side ‘a’ = a3
Problems related to the Volume of cuboid, cube, and cylinder:
Questions: Calculate the length of edge of a cube shaped container of volume 216m3.
Solution: Volume of a cube= a3
=> a3= 216
=> a = 6 m
Question: Calculate the amount of air that can be accumulated in a room which has a length of 5 m, breadth of 6m and a height of 10m.
Solution: Amount of air that can be accumulated in a room = capacity of the room = volume of a cuboid
Volume of cuboid = l×b×h = 5 ×6 ×10 = 300 m3
Thus, this room can accommodate the maximum of 300 m3 of air
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