Question

The length breath and height are in tatio 6:5:4 and the surface area of cuboid is 592m . find the lenght breadth and height of cuboid and volume of cuboid

Answer 1

AnswEr :

• l : b : h = 6 : 5 : 4
• Surface Area = 592 m²
• Find the Dimensions and Volume?

Let the Dimensions Be : length be 6x, breadth be 5x and, height be 4x.

• According to the Question Now :

⇒ Surface Area of Cuboid = 592 m²

⇒ 2(lb + bh + hl) = 592

• Dividing Both term by 2

⇒ lb + bh + hl = 296

• using the ratio values

⇒ (6x × 5x) + (5x × 4x) + (4x × 6x) = 296

⇒ 30x² + 20x² + 24x² = 296

⇒ 74x² = 296

• Dividing Both term by 74

⇒ x² = 4

• squaring root both side

⇒ x = 2 m

_________________________________

• D I M E N S I O N S :

◗ Length = 6x = 6(2m) = 12 m

◗ Breadth = 5x = 5(2m) = 10 m

◗ Height = 4x = 4(2m) = 8m

∴ Length, Breadth and Height will be 12 m, 10 m and 8 m respectively.

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• V O L U M E ⠀O F ⠀C U B O I D :

↠ Volume = Length × Breadth × Height

↠ Volume = 12 m × 10 m × 8 m

↠ Volume = 96 m² × 10 m

↠ Volume = 960 m³

∴ Volume of Cuboid will be 960 m³.

Answer 2

Answer:

$\huge{\underline{\mathfrak{Answer\::}}}$

$\bold{\underline\green{Given\::}}$

☆• L : B : H = 6 : 5 : 4

☆• Surface area of cuboid=592m^2

$\textbf{\underline{To\: find\::}}$

☆• Length, Breadth and height.

☆• Volume of cuboid

$\textbf{\underline{Solution\::}}$

Let the length be 6x , Breadth be 5x and the height be 4x .

According to question:-

2 ( lb + bh + hl) = 592

Or, 2( 6x * 5x + 5x * 4x + 4x* 6x)=592

Or, 30x^2 + 20x^2 + 24x^2 = 592/2

Or, 74x^2 = 296

Or, x^2 = 296/74

Or, x^2 = 4

Or, x = √4

★ x = 2 ★

$\rule{300}{2}$

Length = 6x = 6 × 2 = 12 m ★

Breadth = 5x = 5 × 2 = 10 m ★

Height = 4x = 4 × 2 = 8 m ★

Therefore length, breadth and height are respectively 12 m, 10 m and 8 m.

$\rule{300}{2}$

Volume of cuboid= Length × Breadth × Height

Volume =( 12 × 10 × 8 ) m^3

★ Volume = 960 m^3 ★

Hope it helps you ♥ ♥ ♥