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.

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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:

  1. 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.
  2. 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.
  3. 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.
  4. 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:

  1. Six rectangular faces: A cuboid has six rectangular faces, each with right angles, and opposite faces are congruent.
  2. Opposite faces are parallel and congruent: The opposite faces of a cuboid are parallel to each other and congruent.
  3. Eight vertices: A cuboid has eight vertices, where each vertex is the intersection of three edges.
  4. Twelve edges: A cuboid has twelve edges, which are the line segments connecting its vertices.
  5. Right angles: All angles in a cuboid are right angles.
  6. Rectangular parallelepiped: A cuboid is a type of rectangular parallelepiped, meaning it has six parallelogram faces.
  7. 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.
  8. 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:

  1. Six square faces: A cube has six congruent square faces.
  2. Opposite faces are parallel and congruent: Each pair of opposite faces is parallel and congruent.
  3. Eight vertices: A cube has eight vertices, where three edges meet at each vertex.
  4. Twelve edges: There are twelve edges, connecting the vertices.
  5. Right angles: All angles in a cube are right angles.
  6. Regular polyhedron: A cube is a regular polyhedron, composed of identical polygonal faces with uniform vertices.
  7. Volume: The volume is calculated using V=l3V = l3V=l3, where lll is the length of one side.
  8. Surface area: The surface area is given by S=6l2S = 6l2S=6l2, where lll is the length of one side.
  9. 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

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

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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.