Cube and Cuboid are the most used 3-D shapes in geometry. Cube and cuboid both have 6 faces, 12 edges, and 8 vertices. There are various examples of cubes and cuboids in real life like matchboxes, dice, a box, etc.
In this article, we will learn about cubes and cuboids in detail with their formulas for area and volume as well as diagonals. It also covers the properties of cubes and cuboids along with the solved examples. Let's start our learning on the topic of Cubes and Cuboid.
What is Cube and Cuboid?
Cube and Cuboid are two three-dimensional shapes that have plane surfaces. Both Cubes and Cuboids have 6 faces, 8 vertices, and 12 edges with the difference that cubes have square faces and cuboids have rectangular faces. Let's learn the definitions of cubes and cuboids.
Cube Definition
Cube is a three-dimensional shape that is an extension of the square. In the cube, all the sides are of equal length. A cube consists of 6 faces, 12 edges, 8 vertices, 12 face diagonals and 4 space diagonals. In other words, the shape with equal length, breadth and height is called as a cube. Some of the real-life examples of cube include a dice.
Cuboid Definition
Cuboid is the three-dimensional shape which is an extension of the rectangle. In the cuboid all the sides are length, breadth and height. A cuboid consists of 6 faces, 12 edges, 8 vertices, 12 face diagonals and 4 space diagonals. In other words, the shape with different length, breadth and height is called as a cuboid. Some of the real-life examples of cuboid include a matchbox.
Examples of Cube and Cuboid
There are multiple examples of cube and cuboid in our real-life. Some examples of cube includes a dice, a box etc. Some examples of cuboid includes matchbox, cuboidal box etc.
The different formulas for cube and cuboid including area, and volume; are discussed below in detail.
Surface Area of Cube
Surface Area of the cube can be classified into two:
- Lateral Surface Area
- Total Surface Area
Lateral Surface Area (LSA)
The lateral surface area of the cube is determined by adding the surface area of the faces excluding the top and bottom faces. The formula for the lateral surface area of the cube is given by:
LSA of cube = 4a2
where, a is the side of cube.
Total Surface Area (TSA)
The total surface area of the cube is determined by adding the surface area of all the faces. The formula for the total surface area of the cube is given by:
TSA of cube = 6a2
where, a is the side of cube.
Surface Area of Cuboid
Surface Area of the cuboid can be classified into two:
- Lateral Surface Area
- Total Surface Area
Lateral Surface Area (LSA) of Cuboid
The lateral surface area of the cuboid is determined by adding the surface area of the faces excluding the top and bottom faces. The formula for the lateral surface area of the cuboid is given by:
LSA of cuboid = 2h(l + b)
where,
- l is the length of cuboid,
- b is the breadth of the cuboid
- h is height of cuboid.
Total Surface Area (TSA) Cuboid
The total surface area of the cuboid is determined by adding the surface area of all the faces. The formula for the total surface area of the cuboid is given by:
TSA of cuboid = 2( lb + lh + bh)
where,
- l is the length of cuboid,
- b is the breadth of the cuboid
- h is height of cuboid.
Volume of Cube and Cuboid
Volume is the amount of space occupied by a geometrical shape. Volume in simple terms means the capacity of a solid. The formula to calculate volume of cube and cuboid is discussed below:
Volume of Cube
The volume of a cube is defined by the space bounded by all the sides of the cube. The formula for the volume of the cube is given by:
Volume of cube = a3
where, a is the side of the cube.
Volume of Cuboid
The volume of a cuboid is defined by the space bounded by all the sides of the cuboid. The formula for the volume of cuboid is given by:
Volume of cuboid = l × b × h
- where, l is the length of cuboid
- b is the breadth of the cuboid
- h is height of cuboid.
The diagonal in a cube and cuboid is a line segment that joins the two opposite vertices of a face or two opposite vertices of the body. Based on this there are two types of diagonals Face Diagonals and Body Diagonals. Let's learn this in detail
The formula for Diagonal of Cube is mentioned below:
Face Diagonal of Cube = √2 × side
Body Diagonal of Cuboid = √3 × side
The formula for Diagonal of Cuboid is mentioned below:
Face Diagonal of Cuboid = √{(side1)2 + (side2)2}
Body Diagonal of Cuboid = √(l2 + b2 + h2)
Properties of Cube and Cuboid
Cube and Cuboid possess some significant properties. These properties are discussed in detail below:
Properties of Cube
There are several properties of cube some of these are listed below:
- Cube is the 3-D figure of square.
- All faces of the cube are square in shape.
- Opposite faces are parallel to each other.
- The length of all the edges is equal.
- The sides of the cube intersect each other at right angles.
- The faces of the cube meet each other at right angles.
- The space diagonals of the cube are equal.
Properties of Cuboid
There are several properties of cuboid some of these are listed below:
- Cuboid is the 3-D figure of rectangle.
- All the faces of the cuboid are rectangle in shape.
- Opposite faces and opposite edges are parallel and equal.
- The angles of the cuboid intersect at right angles.
Cube and Cuboid Difference
The main difference between cube and cuboid is tabulated below:
Cube
| Cuboid
|
|---|
Cube is 3-D shape with all sides equal.
| Cuboid is 3- D shape with length, breadth and height.
|
The faces of cube are square in shape.
| The faces of cuboid are rectangle in shape.
|
The length of all edges is equal.
| The length of all edges is unequal.
|
Example of cube is dice.
| Example of cuboid is matchbox.
|
Also, Check
Solved Examples on Cube and Cuboid
Example 1: Find the total surface area of cube if the side of the cube is 4 units.
Solution:
TSA of cube = 6a2
where, a is the side of cube.
a = 4 units
⇒ TSA of cube = 6 × 42
⇒ TSA of cube = 96 sq. units
Example 2: Find the volume of cube if the side of the cube is 2 units.
Solution:
Volume of cube = a3
where, a is the side of cube.
a = 2 units
⇒ Volume of cube = 23
⇒ Volume of cube = 8 cubic unit
Example 3: Find the volume if the length, breadth and height of the cuboid is 9 units, 5 units and 2 units respectively.
Solution:
Volume of cuboid = lbh
where, l is the length of cuboid, b is the breadth of the cuboid and h is height of cuboid.
⇒ Volume of cuboid = 9 × 5 × 2
⇒ Volume of cuboid = 90 cubic units.
Example 4: Find the lateral surface area of cuboid if the length, breadth and height of the cuboid is 4 units, 3 units and 2 units respectively.
Solution:
LSA of cuboid = 2h(l + b)
where, l is the length of cuboid, b is the breadth of the cuboid and h is height of cuboid.
⇒ LSA of cuboid = 2 × 2 × (4 + 3)
⇒ LSA of cuboid = 4 × 7
⇒ LSA of cuboid = 28 sq. units
Practice Questions on Cube and Cuboid
Q1. Find the surface area of cuboid if the length, breadth and height of the cuboid is 14 units, 10 units and 6 units respectively.
Q2. Find the total surface area of cuboid if the length, breadth and height of the cuboid is 6 units, 3 units and 2 units respectively.
Q3. Find the volume of cuboid if the length, breadth and height of the cuboid is 29 units, 11 units and 9 units respectively.
Q4. Find the volume of cube if the side of the cube is 12 units.
Q5. Find the lateral surface area of cube if the side of the cube is 24 units.
Q6. Find the volume of cube if the side of the cube is 8 units.
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