Question

The length breadth and height of a cuboid are in the ratio 7 : 6 : 5 . if the surface area of the cuboid is 1926 cm² find the volume of the cuboid​

Answer 1

Answer :

• Volume of cuboid is 5670cm³

Given :

• The length , breadth and height of a cuboid are in the ratio is 7 : 6 : 5
• Surface area of the cuboid is 1926cm²

To find :

• The volume of the cuboid

Solution :

• Let the length be 7x
• Let the breadth be 6x
• Let the height be 5x

Given that ,

• Surface area of the cuboid is 1926cm²

As we know that

⇢ 2(lb + bh + hl)

⇢ 2((7x)(6x) + (6x)(5x) + (5x)(7x) = 1926

⇢ 2(42x² + 30x² + 35x²) = 1926

⇢ (42x² + 30x² + 35x²) = 1926/2

⇢ 107x² = 963

⇢ x² = 963/107

⇢ x² = 9

⇢ x = √9

⇢ x = 3

Now ,

The length,breadth and height of cuboid are

• Length = 7x = 7(3) = 21cm
• Breadth = 6x = 6(3) = 18cm
• Height = 5x = 5(3) = 15cm

Now we have to find the volume of cuboid

As we know that ,

• Volume of cuboid = l × b × h

⇢ 21 × 18 × 15

⇢ 5670 cm³

Hence Volume of cuboid is 5670cm³

Answer 2

Answer:

5670 cm³

Step-by-step explanation:

Given :

Length : Breadth : Height = 7 : 6 : 5

Hence,

Length (l) = 7x

Breadth (b) = 6x

Height (h) = 5x

TSA of cuboid = 1926 cm²

Procedure :

Formula : TSA of a cuboid = 2[(l × b) + (b × h) + (l × h)] units²

⇒ 1926 cm² = 2 × [(7x × 6x) + (6x × 5x) + (7x × 5x)]

⇒ 963 cm² = [(7x × 6x) + (6x × 5x) + (7x × 5x)]

⇒ 963 cm² = [42x² + 30x² + 35x²]

⇒ 963 cm² = 107x²

⇒ 107x² = 963 cm²

⇒ x² = $\frac{963}{107}$ cm²

⇒ x² = 9 cm²

⇒ x = ± √9 cm

As the values of the dimensions of a cuboid cannot be negative,

∴ x = 3 cm.

Now, calculating the dimensions of the cuboid :

Length = 7x cm = 7 × 3 cm = 21 cm.

Breadth = 6x cm = 6 × 3 cm = 18 cm.

Height = 5x cm = 5 × 3 cm = 15 cm.

Hence the volume of the cuboid is :

Formula : Volume of a cuboid = lbh units³

⇒ V = 21 × 18 × 15 cm³

⇒ V = 3 × 7 × 3 × 6 × 3 × 5 cm³

⇒ V = 27 × 7 × 30 cm³

⇒ V = 189 × 3 × 10 cm³

⇒ V = 567 × 10 cm³

∴ Volume of the cuboid = 5670 cm³.

Thanks !