A cuboid is a three-dimensional shape has six, rectangle-shaped sides. Cuboid also have eight vertices (corners) and twelve edges. The angles in a cuboid are all right angles.
Face diagonals are line segments linking the opposite corners of a face. Each face has two, for a total of 12 in the cuboid. The length of the face diagonals is given by the formula
Length of Diagonal of Face of the Cuboid = √(length2 + breadth2 )
Space diagonals are line segments linking the opposite corners of a cuboid, cutting through its interior. A cuboid has 4 space diagonals. The length of the space diagonal is given by the formula
Length of Diagonal of Cuboid = √(length2 + breadth2 + height2)
The perimeter of a cuboid found by adding all the sides.
Perimeter = 4(length + breadth + height)
If the length, width and height of a cuboid are 5 cm, 3 cm and 2 cm, find its Perimeter.
Perimeter = 4 (5+3+2)
P = 4 (10)
P = 40 cm
The volume of the cuboid is equal to the product of the area of one surface and height. Volume is measured in cubes (or cubic units)
Volume = length × breadth × height
If the length, breadth and height of a cuboid are 5 cm, 2 cm and 4 cm, then find its volume.
V = 5 x 2 x 4
V = 40 cubic cm
Sum of the areas of all its 6 rectangular faces
Surface Area = 2(lb + bh +lh)
The length, width and height of a cuboid are 11cm, 9cm and 15cm respectively. Calculate the total surface area of the cuboid.
TSA = 2 (11*9 + 9*15 + 15*11)
= 2(99 + 135 + 165)
= 2 * 399
TSA = 798cm²
The sum of surface areas of all sides except the top and bottom face of solid is defined as the lateral surface area of a solid.
Lateral surface = 2h(l +b)
Where, l is lenght, b is breadth, h is height
If the length, breadth and height of a cuboid are 5 cm, 3 cm and 4 cm, then find its lateral surface area.
LSA = 2h(l+b)
= 2 x 4(5+3)
= 2 x 4(8)
LSA = 2 x 32 = 64 cm2
Properties of Cuboid:
- It has 12 edges
- It has 8 corners or vertices
- It has 6 faces.
- All faces of the cuboid are in a rectangle shape.
- The angles in a cuboid are all right angles
- The edges opposite to each other are parallel.