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

$\huge\boxed{\fcolorbox{green} {purple}{QUESTION : }}$

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?

$\huge\boxed{\fcolorbox{blue} {orange}{GIVEN : }}$

A cubical box has one of its sides as (2a - b) centimetres.

$\huge\boxed{\fcolorbox{green} {red}{NOTE : }}$

A cube has all sides equal

$\huge\boxed{\fcolorbox{pink} {grey}{WARNING : }}$

Ignore thickness of the walls of the cubical box.

$\huge\boxed{\fcolorbox{green} {green}{SOLUTION :}}$

VOLUME OF CUBE (V) = (side)³

● V = (2a –b)³

○(a–b)³ = a³ -b³ -3ab(a-b)

● V = 8a³ -b³ -3× 2a×b(2a-b)

● V = 8a³ –b³ – 6ab(2a-b)

● V = 8a³ –b³ – 12a²b +6ab² cm³☆

___________

The box has to be painted on all sides so it will cover TOTAL SURFACE AREA of the cube.

●Total Surface Area = 6(side)²

○(a-b)² = a² + b² -2ab

●TSA = 6[ 4a² + b² - 2×2a×b]

●TSA = 6[ 4a² + b² - 4ab ]

●TSA = 24a² + 6b² – 24ab cm²☆

___________

Hope it helps

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$\huge\purple{\mathfrak{@phenom}}$