Question

The surface area of a cuboid is 1792 cm². It's length, breadth and height are in the ratio 4:2:1 respectively. Find its dimensions.​

Answer 1

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

Given:

${\sf{Surface \:area \:of \:cuboid = 1792cm^2}}$

${\sf{Length:Breadth:Height = 4:2:1}}$

To find:

Dimensions of cuboid

Solution:

Its given that length:breadth: height = 4:2:1.

Let the length,breadth and height respectively be 4x,2x and x.

$\boxed{\sf{\red{Surface \:Area\: of \:Cuboid = 2(lb+bh+hl)}}}$

Substituting the values of l,b and h....

$1792 = 2[(4x)(2x)+(2x)(x) + (x)(4x) ]\\ 896 = 8 {x}^{2} + 2 {x}^{2} + 4 {x}^{2} \\ 896 = 14 {x}^{2} \\ {x}^{2} = 896 \div 14 \\ {x}^{2} = 64 \\ x = \sqrt{64}$

$\boxed{x = 8}$

Now ,

length = 4x = 4(8) = 32cm

breadth = 2x = 2(8) = 16cm

height = x = 8cm

Therefore,the length, breadth and height of the cuboid is 32cm, 16cm and 8cm respectively.

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Answer 2

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$\huge\mathfrak\purple{Solution:-}$

Answer:

⏩Dimensions of the cuboid= 32cm × 16 cm × 8 cm.

Step-by-step explanation:

⏩ Let the unknown values of the length, breath and height be,

* l = 4x

*b = 2x

and

*h = 1x

We know that, the surface area of a cuboid= 2(lb + bh + hl)

=) 1792 cm² = 2 (4x × 2x + 2x × 1x + 1x × 4x)

=) 1792 cm² = 2 (8x² + 2x² + 4x²)

=) 1792/2 = 14x²

=) 896 = 14x²

=) 896/14 = x²

=) 64 = x²

=) 8 cm = x

→Hence,

*l = 4x = 4 × 8 = 32 cm

*b= 2x = 2 × 8 = 16 cm

*h = 1x = 1 × 8 = 8 cm.

→Therefore, the required dimensions of the given cuboid is :-

32 cm × 16 cm × 8 cm.

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