[Maths Class Notes] on Difference between Cube and Cuboid Pdf for Exam

In Geometry, we have studied different two-dimensional and three-dimensional figures, like the square, rectangle, circle, cube, cuboid, sphere, and many more. When we look at cube and cuboid at a glance they appear to be the same figure, but some of their properties distinguish them from each other. So let us study what is cube and cuboid, different properties of cube and cuboid, and see what is the difference between cube and cuboid?

What is a Cube?

A cube is a three-dimensional figure composed of square-shaped faces of the same size. All the angles of a cube meet at 900. A cube has 6 equal faces, and all the faces are square-shaped. It has 8 vertices and 12 equal edges.

The below figure represents a cube, where l is length, b is the breadth, and h is height and l = b = h. The length, breadth, and height represent the edges of the cube. And when the three edges meet at a point it is called a vertex.

Properties of Cube

A cube has all its faces square-shaped.
All the faces and edges are equal.
The angles of the cube are at right angles.
Each of the faces meets the other adjacent four faces.
Each of the vertices meets the three faces and three edges.
The edges opposite to each other are parallel and also equal.

What is a Cuboid?

A cuboid is a three-dimensional figure composed of rectangular faces. A cuboid is a box-shaped figure. A cuboid also has 12 edges and 8 vertices. The faces and edges of the cuboid are not equal. On the contrary the opposite faces of the cuboid are equal.

The below figure represents the cuboid. Where l is the length, b is the breadth, and h is the height,

l≠b≠h.

Any face can be the bottom face of the cuboid and the remaining four adjacent faces are called the lateral faces of the cuboid.

Properties of Cuboid

A cuboid consists of six rectangular faces.
Opposite faces of the cuboid are equal.
Opposite edges of a cuboid are equal.
The intersection of three faces is a vertex of a cuboid.
The angles of the cuboid are at right angles.

As we now know, what is a cube? What is a cuboid? Let us study cube and cuboid difference i.e cube vs cuboid.

What is the Difference between Cube and Cuboid

Though cube and cuboid are three-dimensional figures with 12 faces, 12 edges, and 8 vertices, they are different from each other. So let us study what is the difference between a cube and a cuboid? The properties which distinguish them from each other as follows:

Cube Vs Cuboid

S.No	Cube	Cuboid
1	All the edges(sides) of a cube are equal i.e the measures of length, breadth, and height are equal.	All the edges(sides) of a cuboid are not equal i.e the measures of length, breadth, and height are not equal.
2	Cube is a 3-dimensional shape of a square	The cuboid is a 3-dimensional shape of a rectangle
3	All the six faces of a cube are square shapes.	All the six faces of a cuboid are rectangles
4	All the 12 diagonals on the surface are of the same measure	It has 12 diagonals. But in the set of 4 diagonals, 3 diagonals are of different measures
5	All the 4 internal diagonals are equal	It has 4 internal diagonals. But the two pairs are of different measures
6	Examples of the cube are Ice cube, Dice, Rubik’s Cube	Examples of cuboids are Bricks, Duster.
7	Lateral Surface Area = 4 × (edge)2	Lateral Surface Area= 2 (l + b) h where, l = length, b = breadth and h = height
8	Total Surface Area = 6 × (edge)2	Total Surface Area = 2 (lb + bh + hl)where,l = length, b = breadth and h = height
9	Diagonal = √3 × (edge)	Diagonal = [ sqrt{l^{2} + b^{2} + h^{2}}] where, l = length, b = breadth and h = height
10	Volume = (edge)3	Volume = l × b × h where,l = length, b = breadth and h = height
11	Perimeter = 12 (edge)	Perimeter = 4(l + b+ h) where, l = length, b = breadth and h = height

These will make the concept of cube vs cuboid crystal clear.

Solved Examples

Example 1: Find the total surface area of the cuboid with dimensions length = 4 cm, breadth = 3cm, and height = 7 cm.

Solution:

We have,

Tot
al Surface Area of cuboid = 2 (lb + bh + hl )

= 2 ( 4×3 + 3×7 + 7×4)

= 2 ( 12 + 21 + 28 )

= 2 x 61

= 122 cm2

So, the total surface area of this cuboid is 122cm2.

Example 2: Find the surface area of a cube having its sides equal to 5 cm in length.

Solution: Given length = edge = 5 cm

We have, Surface area of cube = 6 ( edge)2

= 6× 52

= 6 × 25

= 150 cm2

Quiz Time

The length, width, and height of a cuboid are 10 cm, 12 cm, and 14 cm respectively. Find the lateral surface area and total surface area of a cuboid.
If the value of the side of the cube is 9cm, then find the surface area and volume of the cube.

Similarities between Cube and Cuboid

The first thing which is similar between cube and cuboid is that they both have six faces.
The next similar thing between a cube and a cuboid is that they both have twelve edges.
The other thing which is similar between them is that they both have eight vertices.

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