What are Cubes and Cuboids?
Objects seen in everyday life such as books, ice cubes, a dice, Rubik’s cubes, a match box and so on, are examples of solids having a cubic or a cuboidal shape.
A cube is a three-dimensional figure composed of square shaped faces of the same size and has an angle of 90 degrees between them. It has 6 faces, 12 edges of same length and 8 vertices. Opposite edges are equal and parallel and each vertex joins three faces and three edges.
A cuboid is a three-dimensional figure that has three pairs of rectangular faces. Like a cube, it has six faces, eight vertices and twelve edges. The opposite faces are congruent. Out of these six faces, two faces are square shaped.
What is the Volume of a Cube?
Volume of any solid shape is the measure of space occupied or enclosed within its faces. The volume of a cube is equal to the amount of space enclosed within its 6 square shaped faces.
The volume of a cube is equal to the product of the area of its square base and its height. As we know, all the edges of the cube are of the same length. Hence,
Volume of the cube = l\(^2\) × h
Since, l = h
Therefore,
Volume of the cube = l\(^2\) × l
Volume of the cube = l\(^3\) cubic units |
What is the Volume of a Cuboid?
Similar to a cube, the volume of a cuboid is equal to the product of the area of its base and height.
Let base area = B and height = h, then,
Volume of a cuboid = Bh
Base area = length × width, so,
Volume of the cuboid = (length × width × height) cubic units
Volume of the cuboid = ( l × w × h) cubic units |
[Note: Volume of any solid shape is measured in cubic units.]
Solved Examples
Example 1: If the length, width and height of a cuboid are 6 centimeters, 4 centimeters and 9 centimeters respectively, then find its volume.
Solution:
Given, Length (l) = 6 cm, Width (w) = 4 cm and Height (h) = 9 cm
Volume of cuboid = l × w × h [Formula for the volume of a cuboid]
V = 6 × 4 × 9 [Substitute values]
V = 216 cm³ [Multiply]
Therefore, the volume of the cuboid is 216 cubic centimeters.
Example 2: Sam made a matchbox with 5 centimeters long, 6 centimeters wide and 4 centimeters in height. Find the volume of the box.
Solution:
A matchbox is cuboidal in shape. So we will use the formula for the volume of a cuboid.
Given: length = 5 cm, width = 6 cm and height = 4 cm
Volume of cuboid = l × w × h [Formula for the volume of a cuboid]
V = 5 × 6 × 4 [Substitute values]
V = 120 cm³ [Multiply]
Therefore, the volume of the matchbox is 120 cubic centimeters.
Example 3: If the length of the side of a cube is 7 meters, then find its volume.
Solution:
Given, side length, l = 7 m
Volume of cube = l\(^3\) [Formula for volume of a cube]
V = 7\(^3\) [Substitute value]
V = 343 m³ [Cube of 7]
So, the volume of the cube is 343 cubic meters.
Example 4: Using the volume of a cube formula, calculate the side length of a Rubik’s cube whose volume is 125 cubic inches.
Solution:
Given: Volume of the Rubik’s cube, V = 125 in\(^3\)
Volume of cube = l\(^3\) [Formula for volume of a cube]
125 = ( l\(^3\) ) [Substitute value]
\(\sqrt[3]{125}\) = l [Cube root on both sides]
5 = l [Cube root of 125 is 5]
So, l = 5 in
Hence, the side length of the Rubik’s cube is 5 inches.
Yes, a cube is a special kind of cuboid in which all the side lengths of the cuboid are equal, that is, ‘length = breadth = height’.
A cube has 2 diagonals on each face, so there are a total of 12 diagonals.
A cuboid is also known as a rectangular prism.
A cube or a cuboid have two types of surface areas, which are, total surface area and lateral surface area.