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.
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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.
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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=l3V = l3V=l3, where lll is the length of one side.
- Surface area: The surface area is given by S=6l2S = 6l2S=6l2, 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.
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Formulas of Cube and Cuboid
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Cube |
Cuboid |
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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) |
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Volume of cube = (Side)3 |
Volume of the cuboid = (l × b × h) |
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Diagonal of a cube = √3(side) |
Diagonal of the cuboid =√( l*l + b*b +h*h) |
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Perimeter of cube = 12 × side |
Perimeter of cuboid = 4 (l + b + h) |
Where as l,b,h represent-: l=Length b=Breadth h=Height
Frequently Asked Questions
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.