Cube and Cuboid
A cube is a three-dimensional shape with six congruent square faces, where each vertex connects three edges of equal length. It is a specific type of rectangular parallelepiped. A cuboid is a three-dimensional shape with six rectangular faces, all at right angles to each other, with opposite faces being congruent. It is also considered a rectangular parallelepiped. If all the faces of a cuboid are squares, then it is also a cube.
Cube and Cuboid Definition
A cube is a three-dimensional solid figure with six equal square faces, eight vertices, and twelve edges. In contrast, a cuboid is a three-dimensional figure with six rectangular faces, which may not all be equal in length. Like a cube, a cuboid also has eight vertices, twelve edges, and six faces. If all the sides of a cuboid are equal, it becomes a cube.
Also Read: Cube Root 1 to 20
Difference Between Cube And Cuboid
The difference between a cube and a cuboid lies in the dimensions of their sides. A cube has equal length, width, and height, with all its faces being squares, making all its edges of equal length. In contrast, a cuboid has unequal length, width, and height, with its faces being rectangles, allowing its edges to have different lengths. In simple terms, a cube is a special type of cuboid where all sides are equal.
Steps to differentiate a cube from a cuboid:
- Measure the sides: Measure the length, width, and height of the solid figure. If all sides are equal, it's a cube. If they are unequal, it's a cuboid.
- Check the faces: Look at the faces of the solid figure. If all faces are square, it's a cube. If they are rectangles, it's a cuboid.
- Compare the edges: Measure the edges of the solid figure. If all edges are equal, it's a cube. If they are unequal, it's a cuboid.
- Consider the angles: Check the angles of the solid figure. If all angles are right angles, it's a cuboid. If all faces are square, it's also a cube.
Shape of Cube and Cuboid
A cube is a three-dimensional geometric shape with six congruent square faces, with all edges and vertices of equal length. In contrast, a cuboid is a three-dimensional shape with six congruent rectangular faces, all meeting at right angles (90°).
Properties of a Cuboid
A cuboid is a three-dimensional shape with the following properties:
- Six rectangular faces: A cuboid has six rectangular faces, each with right angles, and opposite faces are congruent.
- Opposite faces are parallel and congruent: The opposite faces of a cuboid are parallel to each other and congruent.
- Eight vertices: A cuboid has eight vertices, where each vertex is the intersection of three edges.
- Twelve edges: A cuboid has twelve edges, which are the line segments connecting its vertices.
- Right angles: All angles in a cuboid are right angles.
- Rectangular parallelepiped: A cuboid is a type of rectangular parallelepiped, meaning it has six parallelogram faces.
- Volume: The volume of a cuboid can be calculated using the formula V=l x w x hV = l \times w \times hV=l x w x h, where lll is the length, www is the width, and hhh is the height.
- Surface area: The surface area of a cuboid can be calculated using the formula S=2lw+2lh+2whS = 2lw + 2lh + 2whS=2lw+2lh+2wh, where lll, www, and hhh are the length, width, and height of the cuboid.
Also Read: Cube Root Of 1728
Properties of Cube
A cube is a special type of cuboid with these properties:
- Six square faces: A cube has six congruent square faces.
- Opposite faces are parallel and congruent: Each pair of opposite faces is parallel and congruent.
- Eight vertices: A cube has eight vertices, where three edges meet at each vertex.
- Twelve edges: There are twelve edges, connecting the vertices.
- Right angles: All angles in a cube are right angles.
- Regular polyhedron: A cube is a regular polyhedron, composed of identical polygonal faces with uniform vertices.
- Volume: The volume is calculated using V=l^{3}V = l^{3}V=l^{3}, where lll is the length of one side.
- Surface area: The surface area is given by S=6l^{2}S = 6l^{2}S=6l^{2}, where lll is the length of one side.
- Equal length, width, and height: A cube has equal length, width, and height, distinguishing it as a special type of cuboid.
Read More: Cube Root of 216
Formulas of Cube and Cuboid
Cube |
Cuboid |
Total Surface Area = 6(side)2 |
Total Surface area = 2 (l × b + b × h + l × h) |
Lateral Surface Area = 4 (Side)2 |
Lateral Surface area = 2 h(l + b) |
Volume of cube = (Side)3 |
Volume of the cuboid = (l × b × h) |
Diagonal of a cube = √3(side) |
Diagonal of the cuboid =√( l*l + b*b +h*h) |
Perimeter of cube = 12 × side |
Perimeter of cuboid = 4 (l + b + h) |
Where as l,b,h represent-: l=Length b=Breadth h=Height
Related Links
- Derivative of Inverse Trigonometric functions
- Decimal Expansion Of Rational Numbers
- Cos 90 Degrees
- Factors of 48
- De Morgan’s First Law
- Counting Numbers
- Factors of 105
- Cuboid
- Cross Multiplication- Pair Of Linear Equations In Two Variables
- Factors of 100
- Factors and Multiples
- Derivatives Of A Function In Parametric Form
- Factorisation Of Algebraic Expression
- Cross Section
- Denominator
- Factoring Polynomials
- Degree of Polynomial
- Define Central Limit Theorem
- Factor Theorem
- Faces, Edges and Vertices
- Cube and Cuboid
- Dividing Fractions
- Divergence Theorem
- Divergence Theorem
- Difference Between Square and Rectangle
- Cos 0
- Factors of 8
- Factors of 72
- Convex polygon
- Factors of 6
- Factors of 63
- Factors of 54
- Converse of Pythagoras Theorem
- Conversion of Units
- Convert Decimal To Octal
- Value of Root 3
- XXXVII Roman Numerals
- Continuous Variable
- Different Forms Of The Equation Of Line
- Construction of Square
- Divergence Theorem
- Decimal Worksheets
- Cube Root 1 to 20
- Divergence Theorem
- Difference Between Simple Interest and Compound Interest
- Difference Between Relation And Function
- Cube Root Of 1728
- Decimal to Binary
- Cube Root of 216
- Difference Between Rows and Columns
- Decimal Number Comparison
- Data Management
- Factors of a Number
- Factors of 90
- Cos 360
- Factors of 96
- Distance between Two Lines
- Cube Root of 3
- Factors of 81
- Data Handling
- Convert Hexadecimal To Octal
- Factors of 68
- Factors of 49
- Factors of 45
- Continuity and Discontinuity
- Value of Pi
- Value of Pi
- Value of Pi
- Value of Pi
- 1 bigha in square feet
- Value of Pi
- Types of angles
- Total Surface Area of Hemisphere
- Total Surface Area of Cube
- Thevenin's Theorem
- 1 million in lakhs
- Volume of the Hemisphere
- Value of Sin 60
- Value of Sin 30 Degree
- Value of Sin 45 Degree
- Pythagorean Triplet
- Acute Angle
- Area Formula
- Probability Formula
- Even Numbers
- Complementary Angles
- Properties of Rectangle
- Properties of Triangle
- Co-prime numbers
- Prime Numbers from 1 to 100
- Odd Numbers
- How to Find the Percentage?
- HCF Full Form
- The Odd number from 1 to 100
- How to find HCF
- LCM and HCF
- Calculate the percentage of marks
- Factors of 15
- How Many Zeros in a Crore
- How Many Zeros are in 1 Million?
- 1 Billion is Equal to How Many Crores?
- Value of PI
- Composite Numbers
- 100 million in Crores
- Sin(2x) Formula
- The Value of cos 90°
- 1 million is equal to how many lakhs?
- Cos 60 Degrees
- 1 Million Means
- Rational Number
- a3-b3 Formula with Examples
- 1 Billion in Crores
- Rational Number
- 1 Cent to Square Feet
- Determinant of 4×4 Matrix
- Factor of 12
- Factors of 144
- Cumulative Frequency Distribution
- Factors of 150
- Determinant of a Matrix
- Factors of 17
- Bisector
- Difference Between Variance and Standard Deviation
- Factors of 20
- Cube Root of 4
- Factors of 215
- Cube Root of 64
- Cube Root of 64
- Cube Root of 64
- Factors of 23
- Cube root of 9261
- Cube root of 9261
- Determinants and Matrices
- Factors of 25
- Cube Root Table
- Factors of 28
- Factors of 4
- Factors of 32
- Differential Calculus and Approximation
- Difference between Area and Perimeter
- Difference between Area and Volume
- Cubes from 1 to 50
- Cubes from 1 to 50
- Curved Line
- Differential Equations
- Difference between Circle and Sphere
- Cylinder
- Difference between Cube and Cuboid
- Difference Between Constants And Variables
- Direct Proportion
- Data Handling Worksheets
- Factors of 415
- Direction Cosines and Direction Ratios Of A Line
- Discontinuity
- Difference Between Fraction and Rational Number
- Difference Between Line And Line Segment
- Discrete Mathematics
- Disjoint Set
- Difference Between Log and Ln
- Difference Between Mean, Median and Mode
- Difference Between Natural and whole Numbers
- Difference Between Qualitative and Quantitative Research
- Difference Between Parametric And Non-Parametric Tests
- Difference Between Permutation and Combination
Frequently Asked Questions on Cube and Cuboid
Ans. Every cube is a cuboid because it has six faces, twelve edges, and eight vertices, with opposite faces being parallel and congruent rectangles.
Ans. A Rubik's cube is a cube, as it has equal length, width, and height with six congruent square faces.
Ans. The formula for the volume of a cuboid is V=l x w x h, where lll is length, www is width, and hhh is height.
Ans. 3 cuboid typically refers to three-dimensional shapes with rectangular faces, but without more context, it is unclear what specific property or calculation is being asked about.