Cube and Cuboid: In our daily life, we see many objects like notebooks, matchboxes, instrumental geometry boxes, cones, cricket balls, cylinders, etc. These are all three-dimensional objects (solid shapes). All these objects occupy some shape and have three dimensions Length, Breadth, Height, or Depth.

Moreover, we often find some shapes with two or more identical (congruent) faces. For example, the Cube has squared faces on each side, and the Cuboid has rectangular faces on each side. A Cube and Cuboid is a three-dimensional shape with six faces, eight vertices, and twelve edges. The main distinction is that a cube has the same length, width, and height on all sides, whereas a cuboid has varied length, breadth, and height. Both shapes appear to be nearly the same, however, they have different properties.

In this article, we will dive deep into the concept of Cubes and Cuboids, Definition, Properties, Examples, etc. Continue reading to know more.

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Difference Between Cube and Cuboid

A square is a two-dimensional figure with two dimensions length and breadth, while a cube is a three-dimensional figure with three dimensions length, breadth, and height. The side faces of a cube are formed by squares. Also knowing the cube and cuboid formula will enable students to know the difference between cube and cuboid easily.

Common examples of Cube in real life are square ice cubes, dice, sugar cubes, Rubik’s cube etc.

A cube shape is like that of perfect square. Cube is a three-dimensional box-like figure represented in the three-dimensional plane. Cube has \(6\) square-shaped equal faces. Each face meets another face at \({\rm{9}}{{\rm{0}}^{\rm{o}}}\) each. Three sides of the cube meet at the same vertex.

In the given figure, faces, edges and vertices of a cube have been shown. \(8\) corners of the cube are its vertices. The line segments forming the cube are its \(12\) edges. The six square faces forming the cube are its \(6\) faces.

Faces of a Cube:  Polygon regions forming a solid are called its faces.

Edges of a Cube: Line segments where the faces meet are called its edges.

Vertices of a Cube: Points of intersection of three faces of a solid are called its vertices.

Net of a Cube

The net of a solid is a diagram drawn on paper which when cut and folded along the lines can be used to construct a solid shape. Net of a Cube is a two-dimensional shape that can be folded into a three-dimensional figure is a Cube.

A Cube consists of \(6\) square faces, \(12\) edges, and \(8\) vertices. When the square faces of a cube are separated at the edges and laid out flat, they make a two-dimensional figure called a net.

Formulas of a Cube

Lateral Surface Area of a Cube:

Consider a Cube of edge length \(‘a’\), then, the area of each face of a square \( = {a^2}\)
So, the Lateral Surface Area of a Cube \( = \) Sum of the area of all \(4\) side faces
Lateral Surface Area(LSA) \( = 4{a^2}\) square units

Total Surface of a Cube

We know the cube consists of \(6\) square faces. Let us consider if each side of a cube is \(a\), then the total surface area of the Cube is \( = 6{a^2}\).
Total Surface Area (TSA) \( = 6{a^2}\) square units

Volume of a Cube

The volume of a cube can be found by multiplying the edge length three times. If each edge length is \(“a”\), then the Volume of a Cube is \({a^3}\).
\(V = {a^3}\) cubic units

Cuboid

A rectangle is a two-dimensional figure with two dimensions length and breadth, while a cuboid is a three-dimensional figure with three dimensions length, breadth, and height. The side faces of a cuboid are formed by rectangles.

Common examples of cuboid in real life are bricks, the lunch box, notebook, and Geometry instrumental box.

Cuboid is a three-dimensional box-like figure represented in the three-dimensional plane. Cuboid has \(6\) rectangular-shaped equal faces. Each face meets another face at \({\rm{9}}{{\rm{0}}^{\rm{o}}}\) each. Three sides of the cuboid meet at the same vertex.

Net of a Cuboid

A cuboid consists of \(6\) rectangular faces, \(12\) edges, and \(8\) vertices. When the rectangular faces of a cuboid are separated at the edges and laid out flat, they make a two-dimensional figure called a net of a Cuboid. A cuboid shape is like that of a rectangular shoe box.

Formulas of a Cuboid

Lateral Surface Area of a Cuboid

Lateral Surface Area of a cuboid  \( = \)  Sum of four vertical sides

Lateral Surface Area (LSA)\( = 2(1 + b)h\) square units

Total Surface of a Cuboid

We know the cuboid consists of \(6\) rectangular faces.

Total Surface Area (TSA) \( = 2(lb + bh + hl)\) square units

Where, \(l = \) length, \(b = \) breadth, \(h = \) height

Volume of a Cuboid

Volume of a cuboid is \(V{\rm{ = length \times breadth \times height}}\)

\(V = \left( {l \times b \times h} \right)\) Cubic units

Difference Between Cube and Cuboid

Cube	Cuboid
In a Cube, all six faces are squares.	In a cuboid, all six faces are rectangles.
The measurement of length, breadth, and height in a Cube is equal, i.e. sides/edges are equal.	The measurement of length, breadth, and height are not equal, i.e., sides/edges are not equal.
A cube has \(12\) diagonals in total with surface area measured the same.	A cuboid has \(12\) diagonals in total, where \(3\) diagonals are different in the measure.
In a cube, the \(4\) internal diagonals should have the same measure.	In a cuboid, among the \(4\) internal diagonals, two pairs of the internal angles are of different measurement.
Volume of a Cube \( = {({\rm{Side}})^3}\)	Volume of a Cuboid \({\rm{ = length \times breadth \times height}}\)
Rubik’s cube, Dice, ice cube are a few examples	Bricks, pencil box, lunch box, are a few examples of a cuboid

Solved Examples – Cube and Cuboid Formula

Q.1. Find the volume of the cube whose each edge is \({\rm{5}}\,{\rm{cm}}\).
Ans: From the given edge \(a = 5\;{\rm{cm}}\)
Volume of a Cube is \({a^3}\).
\(V = {a^3}\) cubic units
\( \Rightarrow V = {5^3}\)
\( \Rightarrow V = 125\;{\rm{c}}{{\rm{m}}^3}\)
Hence, the volume of a Cube is \(125\;{\rm{c}}{{\rm{m}}^3}\).

Q.2. Find the volume of the cuboid whose dimensions are length \({\rm{ = 6}}\,{\rm{m}}\), breadth \({\rm{ = 6}}\,{\rm{m}}\), height \({\rm{ = 6}}\,{\rm{m}}\).
.Ans: Given: \({\rm{ = 6\;m,}}\,\,{\rm{breadth = 4\;m,}}\,{\rm{height = 3\;m}}\)
Volume of a Cuboid \({\rm{ = length \times breadth \times height}}\)
\( \Rightarrow \) Volume of a Cuboid \( = 6 \times 4 \times 3\)
\( \Rightarrow V = 72\;{{\rm{m}}^3}\)
Hence, the volume of a Cuboid is \(72\;{{\rm{m}}^3}\).

Q.3. Find the surface area of a cube whose edge is  \(6\;{\rm{cm}}\).
Ans: From the given \( = 6\;{\rm{cm}}\)
The total surface area of the Cube is \(6{a^2}\).
Total Surface Area (TSA)\( = 6 \times {(6)^2}\) square units
\( = 6 \times 36 = 216\;{\rm{c}}{{\rm{m}}^2}\)
Hence, the surface area of a Cube is \(216\;{\rm{c}}{{\rm{m}}^2}\).

Q.4. What is the lateral surface area of a cube of edge \(10\;{\rm{cm}}\)
Ans: From the given \( = 10\;{\rm{cm}}\)
The Lateral Surface Area of a Cube \( = \) Sum of area of all \(4\) side faces
Lateral Surface Area(LSA) \( = 4{a^2}\) square units
\( \Rightarrow {\rm{LSA}} = 4 \times {10^2}\)
\( \Rightarrow {\rm{LSA}} = 4 \times 100\)
\( \Rightarrow {\rm{LSA}} = 400\;{\rm{c}}{{\rm{m}}^2}\)
Hence, the obtained lateral surface area of a cube is \(400\;{\rm{c}}{{\rm{m}}^2}\).

Q.5. A cuboid-shaped wooden block has \({\rm{5}}\,{\rm{cm}}\) length, \({\rm{4}}\,{\rm{cm}}\) breadth and \({\rm{5}}\,{\rm{cm}}\) height. Find the total surface area of a Cuboid.
Ans: Given: Length \({\rm{5}}\,{\rm{cm}}\), Breadth \({\rm{4}}\,{\rm{cm}}\), Height \({\rm{5}}\,{\rm{cm}}\)
Total Surface Area (TSA) \( = 2\left( {lb + bh + hl} \right)\) square units
\( \Rightarrow {\rm{TSA}} = 2(5 \times 4 + 4 \times 1 + 1 \times 5)\)
\( \Rightarrow {\rm{TSA}} = 2(20 + 4 + 5)\)
\( \Rightarrow {\rm{TSA}} = 2(29)\)
\( \Rightarrow {\rm{TSA}} = 58\;{\rm{c}}{{\rm{m}}^2}\)
Hence, the obtained total surface area of a Cuboid is \(58\;{\rm{c}}{{\rm{m}}^2}\).

Q.6. Find the volume of a Cuboid of length \(20\;{\rm{cm}}\), breadth \(12\;{\rm{cm}}\), height \(10\;{\rm{cm}}\).
Ans: Given: length \( = 20\;{\rm{cm}}\), breadth \( = 12\;{\rm{cm}}\), height \( = 10\;{\rm{cm}}\).
Volume of a Cuboid \({\rm{ = length \times breadth \times height}}\)
\( \Rightarrow V = 20 \times 12 \times 10\)
\( \Rightarrow V = 2400\;{\rm{c}}{{\rm{m}}^3}\)
Hence, the obtained volume of a Cuboid is \(2400\;{\rm{c}}{{\rm{m}}^3}\).

PRACTICE QUESTIONS ON CUBE AND CUBOID

Summary

Cube and Cuboid are three-dimensional figures formed with six faces, eight vertices and twelve edges. The measurement of length, breadth, and height in a Cube is equal but not equal in a Cuboid. In this article, we discussed in detail the shapes, figures, examples nets, and formulas of Cube and Cuboid. The difference between the Cube and Cuboid helps to compare and understand these two. This article helps to solve the problems based on the Cube and Cuboid by using suitable formulas.

Frequently Asked Questions on Cube and Cuboid

We have provided some frequently asked questions about cube and cuboid here:

Q.1. What is the formula of volume of cube and cuboid?
Ans:  The volume of a cube can be found by multiplying the edge length three times. If each edge length is \(“a”\), then the Volume of a Cube is \({a^3}\).
[V = {a^3}] cubic units
And, Volume of a cuboid is:
\(V{\rm{ = length \times breadth \times height}}\)
\(V = \left( {l \times b \times h} \right)\) Cubic units.

Q.2. What is the surface area of cube and cuboid?
Ans: Formulas on the Surface area of cube are:
Lateral Surface Area (LSA) \( = 2(l + b)h\) squre units.
Total Surface Area(TSA) \( = 6{a^2}\) square units.
Formulas on the Surface area of cuboid are:
Lateral Surface Area (LSA) \( = 2(l + b)h\) h squre units.
Total Surface Area (TSA) \( = 2\left( {lb + bh + hl} \right)\) square units.

Q3. Can a cuboid have all rectangular faces?
Ans: Yes, a cuboid consists of \(6\) rectangular faces.

Q.4. Can a cube be called a cuboid?
Ans: Yes, Cubes are also a type of cuboid that has its faces in square shape.

Q.5. What is the difference between a cube and cuboid?
Ans: In a Cube, all the six faces are squares and, in a cuboid, all six faces are rectangles.

Q.6. Do Cuboids have square faces?
Ans: Yes, Cuboids have square faces. The square cuboid, square box is a special case of the cuboid in which at least two faces are squares.

Q.7. How many cubes are in a cuboid?
Ans: If the cuboid is formed with two layers and the length of the first layer is \(6\) and breadth is \(4\):
The number of cubes in the first layer  \( = 6 \times 4 = 24\)
Therefore, the number of cubes in both the layers  \( = 2 \times 24 = 48\)
Hence, \(48\) cubes are there in a Cuboid which consists of two layers, and the length of the first layer is \(6\) and breadth is \(4\).

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