CLASS-9
VOLUME & SURFACE AREA OF SOLID - CUBE
CUBE –
A cuboid whose length, breadth, and height are all equal is called a cube. Ice-cubes, sugar cubes, dice, etc are all examples of a cube. Each edge of a cube is called its side. Let us consider a cube of edge = a units. Then –
Volume of the cube = a³ cubic units
Diagonal of the cube = (a√3) units
Total surface Area of the cube = (6a²) sq. units
Lateral surface area of the cube = (4a²) sq. units
Example.) Find the volume, the total surface area, the lateral surface area, and the length of the diagonal of a cube each of whose edges measures 30 cm.
Ans.) Volume of the cube = a³ cubic units
= (30 X 30 X 30) cm³ = 27000 cm³
The total surface area of the cube = (6a²) sq.units
= (6 X 30 X 30) cm² = 5400 cm²
Lateral surface area of the cube = (4a²) sq.units
= (4 X 30 X 30) cm² = 3600 cm²
Diagonal of the cube = (√3 a) cm = (1.732 X 30) cm
= 51.96 cm (Ans.)