ᴀᴋᴀɴsʜ ʜᴇʀᴇ!QUESTION: A cubical box has one of its sides

1.	ᴀᴋᴀɴsʜ ʜᴇʀᴇ!QUESTION: A cubical box has one of its sides as (2a - b) centimetres. What will be the volume of the box if we don’t consider the thickness of the walls of the box? If the box has to be painted outside on all the sides, what will be the surface area to be painted?
Answer» Length of side of a cubical box = (2a - b) cm Note : Each and every side of a cube are equal to each other Warning : Ignore thickness of the walls of cubical box Volume of a cube (V) = (side)³ ➠ V = (2a - b)³ (a - b)³ = a³ - b³ - 3AB(a-b) ➠ V = (2a)³ - b³ - 3(2a)b(2a-b) ➠ V = 8a³ - b³ - 12a²b - 6ab² ➠ V = 8a³ - b³ - 6ab(2a - b) cm³ The box has to be painted outside on all the sides , so it will covers total SURFACE area of the cube . Total Surface Area of the cube (TSA) = 6 (side)² ➠ TSA = 6 (2a - b)² (a - b)² = a² + b² - 2ab ➠ TSA = 6 [(2a)² + b² - 2(2a)(b)] ➠ TSA = 6 [4a² + b² - 4ab] ➠ TSA = 24a² + 6b² - 24AB cm²

ᴀᴋᴀɴsʜ ʜᴇʀᴇ!QUESTION: A cubical box has one of its sides as (2a - b) centimetres. What will be the volume of the box if we don’t consider the thickness of the walls of the box? If the box has to be painted outside on all the sides, what will be the surface area to be painted?

Answer»

Length of side of a cubical box = (2a - b) cm

Note : Each and every side of a cube are equal to each other

Warning : Ignore thickness of the walls of cubical box

Volume of a cube (V) = (side)³

➠ V = (2a - b)³

(a - b)³ = a³ - b³ - 3AB(a-b)

➠ V = (2a)³ - b³ - 3(2a)b(2a-b)

➠ V = 8a³ - b³ - 12a²b - 6ab²

➠ V = 8a³ - b³ - 6ab(2a - b) cm³

The box has to be painted outside on all the sides , so it will covers total SURFACE area of the cube .

Total Surface Area of the cube (TSA) = 6 (side)²

➠ TSA = 6 (2a - b)²

(a - b)² = a² + b² - 2ab

➠ TSA = 6 [(2a)² + b² - 2(2a)(b)]

➠ TSA = 6 [4a² + b² - 4ab]

➠ TSA = 24a² + 6b² - 24AB cm²