Exams Prep Master
The basic difference between cube and cuboid is that a cube has six square-shaped faces which are of the same size whereas, a cuboid has six rectangular-shaped faces. Although both cube and cuboid look similar structure-wise, they have a few different properties depending on edge length, diagonals, and faces. There are many shapes in geometry such as cylinder, sphere, and cone that have distinct properties but only cuboid and cube are two such solids that have certain common properties like both have six faces, eight vertices, and twelve edges. Moreover, all the interior angles are equal to 90 degrees. Let us study how cubes and cuboids can be distinguished from each other, and discuss some important questions.
| Table of Content |
Key Takeaways- Cube, cuboid, important formulas, properties, the difference between cube and cuboid, examples.
Read More: Trigonometry Table
What is Cube?
A cube is a square but this is the 3-D version of a square. It has 6 faces and all the faces are equal. It is a Hexahedron. All the faces of the cubes are similar. In simple words, a cube is just a square shape. Examples- Rubik’s cube, an ice cube, dice and sugar cubes, etc.
Properties of a Cube
Some of the properties of the cube are as follows:
- A cube has 12 edges and six faces and all of these are equal in their length.
- It’s like a square shape box
- All the angles are in their right angle.
- All the vertex of the cube meets three edges and three faces.
- All the opposite edges are parallel towards the other.
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What are Cuboids?
A cube is made up of three pairs of rectangular shapes. Is cuboid consists of 12 horizons, 8 vertices, and 3 pairs of rectangular. The polyhedron graph of a cuboid is similar to a cube. It’s a 3-D shape rectangular. Examples- A floppy cube, a wooden box, a matchbox, shoebox, book, mattresses, etc.
Properties of Cuboids
Some of the properties of cuboids are given below:
- There are 6 rectangles in cuboids.
- Cuboids are made of 12 edges, 8 rectangles faces.
- It has three dimensions they ought, width & length.
- It has 8 vertices which are 90°.
- It can have 4 rectangular and 2 Square surfaces.
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Difference Between Cube and Cuboid
The difference between a cube and a cuboid can be explained through the following table:
| Cube | Cuboid |
|---|---|
| A cube is a six-squared shape. | Cuboids have rectangular faces. |
| A cube is a 3-D shape square. | Cuboids are a 3-D shape rectangular. |
| It’s a 3-dimensional shape of a square. | Cuboids is a 3-dimensional rectangular. |
| A cube is equal from all its ends. | Cuboid is not equal from all his ends. |
| All the diagonals of a cube are the same. | All the diagonals are not the same in measurement |
| Examples= Dice, Rubik's cube, ice cubes, sugar cubes, gift boxes, cube billing blocks, old iron lockers, chocolate cubes, etc. | Examples= Book, Bricks, mattresses, refrigerators, microwaves, shoebox, lunch boxes, radio, etc. |
| The TSA(Total surface area) formula = 6 × side2 | The TSA (Total surface area) formula = 2 [length.breadth+breadth.height+heigth.length] |
| The LSA (Lateral surface area) formula = 4 x (side)2 | The LSA (Lateral surface area) formula = 2length+breadhheight |
| The volume of a cube = a3 | The volume of Cuboids = v=1×b×h |
| The diagonal formula = 3 × (side) | The diagonal formula = √(length2+ breadth2 +height2) |
| The perimeter formula = 12 (side) | The perimeter formula = 4 (length+breadth+height) |
Cube and Cuboid Similarities
The cube and cuboid are a way similar to each other but they are different when it comes to their measurement. Moreover, a cube and a cuboid have six faces. They both have 12 edges. Cube and cuboid have eight vertices.
Also read: Isosceles Triangle Theorems
Solved Examples
Ques: Find out the volume of a cube if its edge is 7cm.
Solution: edge= a, a=7cm
The volume of the cube is a3
V = a3
=>V=73
=>V=343 cm
The volume of the cube will be 343 cm.
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Ques: Find the amount of water that is stored in an ice cube whose side length is 3 inches.
Solution: Length of the Ice-cube= 5 inches
The amount of water stored= volume of the cube
V = a3
=>V=33
=>V=27 in3
Thus, the amount of water stored in the ice cube is 27in.
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Ques: Find out the total surface area of a Cuboid if it’s length, width & height is 7, 5, 6 respectively.
Solution: length= 7cm
Width= 5cm
Height= 6cm
The total surface of the cuboid= 2[l×w+w×h+(h×l)]
Difference between Cube & Cuboid
TSA = 27×5+5×6+6×7
= 235+30+42
= 2107
=2×107
= 214 cm2
Thus, the total surface area of the cuboids is 214 cm2.
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Things to Remember
- Cubes are square while cuboids are rectangular. An ice cube, a Rubik’s cube are examples of a cube. A matchstick and A lunch box is an example of a cuboid.
- A 3-D square is a cube while A 3-D rectangular is a cuboid. A cube and cuboid can look a little similar but do not get confused. They both have different lengths, heights & widths.
- A cuboid is a three-dimensional figure that has three pairs of rectangular faces attached opposite to each other. These opposite faces are the same.
- The other names for cuboids are rectangular boxes, rectangular parallelepipeds, and right prisms.
Read More:
Sample Questions
Ques: Write the perimeter formula of a cuboid. (2 marks)
Ans: The perimeter for the formula of a cuboid is: 4l+b+h
Where, l= length
b=breadth
h=height
Thus, it is 4 length + breadth + height
For example l=7, b=5, h=9
The perimeter formula= 4l+b+h
= 47+5+9
= 421
= 84 in.
Read More:
Ques: The following properties of cuboid-shaped wooden boxes are given: length= 7cm, height=7cm, breadth= 6cm. Find out the total surface area of a cuboid. (3 marks)
Ans: Length= 7 cm
Breadth= 6 cm
Height= 7 cm
The surface area of cuboids= 2 [length.breadth+breadth.height+height.length]
= 27×6+6×7+7×7
= 242+42+49
=2133
= 266 cm
Thus the total surface of the wooden block is 266 cm.
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Ques: Find out the volume of a cube whose length is 40mm. (2 marks)
Ans: The length given is 40 volumes. The volume of a cube= a3
= 40×40×40 mm3
= 64,000 mm3
Thus, the volume of the cube is 64,000 m.
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Ques: The sides of some cubes are given. Find there volume. (5 marks)
12.5 cm, 3.9 cm, 24.3cm, 10cm
Ans: The Side of the cube= 12.5 cm
The volume of the cube= side3
= 12.53
= 1953.125 cm3
The side of the cube= 2.9 cm
The volume of the cube= side3
= 2.93
= 24.389 cm3
The side of the cube= 24.3 cm
The volume of the cube= side3
= 24.33
= 14,348.907 cm3
The side of the cube= 12 cm
The volume of the cube= side3
= 123
= 1,728 cm3
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Ques: How many cubic meters of water can a cube-shaped tank of 8 m hold? (2 marks)
Ans: The side of a cube-shaped tank= 6 m
The volume of the tank= side3
= 83 m3
= 512 m3
Thus, a cube-shaped tank can hold 512 m3 of water.
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Ques: How do you describe the surface area of a cube or cuboid? (2 marks)
Ans: The area that is occupied by the surfaces of a cube is the surface area of a cube. It is the sum of all the areas of a cube.
The area that is occupied by the surface of a cube is the surface of a cuboid. It is the sum of all the properties of a cuboid like length, breadth & height.
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Ques: Write the Diagonal formula of a cube. (2 marks)
Ans: A cube has a total of 6 faces. So the diagonal faces of a cube are 12 because every face has 2 diagonals.
The diagonal formula of a Cube can be calculated with the help of the length of the cube.
The Diagonal formula of a Cube = 3 × side2
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Ques: Write down some of the daily life examples of Cuboids. (2 marks)
Ans: We can find a lot of cuboid shapes around us in our daily life. Here we are listing the top 10 examples of a cuboid-
- Refrigerator
- Aquarium
- Matchbox
- Books
- Bricks
- Lunch box
- Microwave
- Radio
- Deck cards
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