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 1

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  $\pink{\bigstar}$

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  $\orange{\bigstar}$

Answer 2

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

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