Question

the the surface area of a cuboid is 1372 CM square if the dimensions are in the ratio of 4:2: 1 find the volume of of find the volume and the dimensions of the cuboid​

Answer 1

Step-by-step explanation:

Let l,b,h be 4x,2x,x

TSA=2(lb+bh+hl)

1372=2(8x

2

+2x

2

+4x

2

)

686=14x

2

49=x

2

so x=7

l,b,h = 28,14,7

Answer 2

Answer:

◩ The dimensions are :

• l (length) = 28cm.
• b (breadth) = 14cm.
• h (height) = 7cm.

◩ The volume of the cuboid is :

• 2,744cm²

Step-by-step explanation:

Given that,

• The surface area of a cuboid is 1372cm²
• The dimensions are in ratio 4 : 2 : 1

To find :

• The volume of the cuboid.

Solution :

Let's assume that,

➡ l (length) = 4x

➡ b (breadth) = 2x

➡ h (height) = 1x

We know that,

➡ Surface area of cuboid = 2(lb + bh + hl)

According to the question

$\sf : \implies \: 1372 = 2 \{(4x)(2x) + (2x)(1x) + (4x)(1x) \}$

$\sf : \implies \: 1372 = 2 \{ {8 {x}^{2} + {2x}^{2} + {4x}^{2} }^{} \}$

$\sf : \implies \: 1372 = 2 \{ {14x}^{2} \}$

$\sf : \implies \: 1372 = {28x}^{2}$

$\sf : \implies \: \frac{1372}{28} = {x}^{2}$

$\sf : \implies \: {x}^{2} = 49$

$\sf : \implies \: x = \sqrt{49}$

$\sf : \implies \: x = 7cm$

Therefore :

➡ l (length) = 4x = 28cm.

➡ b (breadth) = 2x = 14cm

➡ h (height) = 1x = 7cm.

Now,

We need to find the volume :

We know that :

➡ Volume of a cuboid = l × b × h

➡ 28 × 14 × 7

➡ 2,744cm²