Surface Area and Volume of a Cube and Cuboid A cube and a cuboid are two-dimensional shapes with six and four sides, respectively. Understanding their surfac...
A cube and a cuboid are two-dimensional shapes with six and four sides, respectively. Understanding their surface area and volume is crucial in various applications like architecture, art, and everyday life.
Surface Area:
The surface area is the total area of all the sides and faces of a shape. For a cube and cuboid, these areas are the same because they have equal sides and equal number of faces.
Area of a Cube: Each side of a cube measures a side length, s. The surface area of a cube with side length s is calculated by multiplying the area of a single side by 6:
Surface Area of a Cube = s² × 6
Area of a Cuboid: Each face of a cuboid measures the side length of the square. The surface area of a cuboid with side length s is calculated by multiplying the area of one face by 4:
Surface Area of a Cuboid = s² × 4
Volume:
The volume is the amount of space inside a 3D shape. For a cube and cuboid, the volume is the same because they have equal dimensions and shape.
Volume of a Cube: The volume of a cube with side length s is calculated by cubing the side length:
Volume of a Cube = s³
Volume of a Cuboid: The volume of a cuboid with side length s is calculated by multiplying the area of one face by the length of the side:
Volume of a Cuboid = s² × length
Examples:
A cube with side length 3 cm has a surface area of 9 cm² and a volume of 27 cm³.
A cuboid with side length 4 cm and side length 5 cm has a surface area of 40 cm² and a volume of 40 cm³