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Updated on 24th July, 2023 , 4 min read
We study many forms and figures in mathematics, such as cylinders, squares, cones, rectangles, and many more. Each of these forms and figures has unique qualities and formulae that we utilize while solving geometry problems in mathematics. Two such forms, the cube, and the cuboid are regarded as comparable yet distinct in their attributes.
Cube: A cube is a three-dimensional shape with six square-shaped sides of equal size and a 90-degree angle between them. It has six faces, twelve edges, and eight vertices. The opposite edges are parallel and equal. Each vertex is intersected by three faces and three edges.
Cuboid: A three-dimensional shape with three pairs of oppositely connected rectangular faces. These two faces are the same. Two of the six faces can be squares. Cuboids are also known as rectangular boxes, rectangular parallelepipeds, and right prisms.
The following table shows the examples of cube and cuboid-
Cube | Cuboid |
Rubik's Cube Square Ice Cubes Dice Sugar Cubes | Refrigerator Matchbox Books Bricks Lunch box |
The following table shows the properties of cubesa and cuboids-
Properties of Cube | Properties of Cuboid |
All of the faces are square. | All of the faces are rectangular. |
All of the faces and edges are the same. | The opposing faces and edges are equal. |
The angles are perpendicular. | The angles are perpendicular. |
Each of the faces intersects with the other four neighboring faces. | At the rim, two faces collide. |
Three faces and three edges are intersected by the vertices. | A vertex is formed by the intersection of three faces. |
The following table shows the parameters on which cube and cuboid should be differentiated-
Parameters | Cube | Cuboid |
Sides | All sides are of the same length. | All sides are of distinct lengths. |
Shape | 3-D representation of a square. | A 3-D representation of rectangle. |
Faces | 6 | 6 |
Diagonals | 12 | 12 face diagonals and 4 body/space diagonals. |
Internal Diagonals | The length of all four internal diagonals should be the same. | A cuboid has four interior diagonals. The two sets of internal angles have distinct measurements. |
Examples | Rubik's Cube, Dice, Ice cube | Bricks, Duster |
LSA (Lateral Surface Area) Formula | 4 × (Side)² | 2 (length + breadth) × height |
TSA (Total Surface Area) Formula | 6 × (Side)² | 2 [(length × breadth) + (breadth × height) + (height × length)] |
Diagonal Formula | √3 × (side) | √(length² + breadth² + height²) |
Volume Formula | (Side)³ | length × breadth × height) |
Perimeter Formula | 12 × (Side) | 4 × (length + breadth + height) |
The formula for calculating the diagonal of a cuboid = Diagonal formula = √(length2+ breadth2+ height2)
= √(802+ 362+ 212)
= √(6400 + 1296 + 441)
= √8137
= 90.2 cm
Therefore, the diagonal of a cuboid is 90.2 cm
Given the length, ‘a'= 4 cm
Surface area = 6a²
= 6 × (4)²
= 6 × 16
= 96 cm²
The formula for calculating the volume of a cuboid is-
Volume = length x breadthx height in cubic units
= 71 x 4 x 29
= 284 x 29
= 8236 cm³
Volume = (side)³cubic units is the formula for calculating the volume of a cube.
Volume = (21)³
= 9261 cm³
As a result, the volume of a cuboid is 8236 cm³,and that of a cube is 9261 cm³. The volume of the cube is significantly more than the volume of the cuboid.
Volume of the room = 523 m³
Area of the floor (l × b) = 210 m²
Therefore, the height of the room = (Volume of the room)/(area of the floor)
= 523/210
= 2.49 m
Total Surface Area (TSA) of cuboid = 2 (lb + bh + hl)
TSA = 2 (8×6 + 6×4 + 4×8)
TSA = 2 (48 + 24 + 32)
TSA = 104
Therefore, the total surface area of this cuboid is 104 sq. cm.
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