Question

The dimensions of a cuboid are in the ratio of 5:3:2 and its
total surface area is 248 m2. The volume of cuboid is​

Answer 1

Given:

The dimensions of a cuboid are in the ratio of 5:3:2 and its  total surface area is 248 m².

To find:

The volume of the cuboid

Solution:

Formulas to be used:

$\boxed{\bold{Volume\:of\:a\:cuboid = length\times breadth\times height}}$

$\boxed{\bold{Total\:Surafce\:Area\:of\:a\:cuboid = 2[(l\times b) + (b\times h) + (l \times h )]}}$

Let's assume,

"5x" → represents the length of the cuboid

"3x" → represents the breadth of the cuboid

"2x" → represents the height of the cuboid

We have,

The total surface area of a cuboid = 248 m²

∴ $2[(l\times b) + (b\times h) + (l \times h )] = 248$

$\implies 2[(5x\times 3x) + (3x\times 2x) + (5x \times 2x )] = 248$

$\implies 2[15x^2 + 6x^2 + 10x^2] = 248$

$\implies 2[31x^2 ] = 248$

$\implies62x^2 = 248$

$\implies x^2 = 4$

$\implies \bold{x = 2}$

Therefore,

Length = 5x = 5 × 2 = 10 m

Breadth = 3x = 3 × 2 = 6 m

Height = 2x = 2 × 2 = 4 m

Now,

The volume of the cuboid is,

= length × breadth × height

= 10 × 6 × 4

= 240 m²

Thus, the volume of the cuboid is → 240 m².

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Answer 2

Given:

The dimensions of a cuboid are in the ratio of 5:3:2 and its  total surface area is 248 m².

To find:

The volume of the cuboid

Solution:

Formulas to be used:

$\boxed{\bold{Volume\:of\:a\:cuboid = length\times breadth\times height}}$

$\boxed{\bold{Total\:Surafce\:Area\:of\:a\:cuboid = 2[(l\times b) + (b\times h) + (l \times h )]}}$

Let's assume,

"5x" → represents the length of the cuboid

"3x" → represents the breadth of the cuboid

"2x" → represents the height of the cuboid

We have,

The total surface area of a cuboid = 248 m²

∴ $2[(l\times b) + (b\times h) + (l \times h )] = 248$

$\implies 2[(5x\times 3x) + (3x\times 2x) + (5x \times 2x )] = 248$

$\implies 2[15x^2 + 6x^2 + 10x^2] = 248$

$\implies 2[31x^2 ] = 248$

$\implies62x^2 = 248$

$\implies x^2 = 4$

$\implies \bold{x = 2}$

Therefore,

Length = 5x = 5 × 2 = 10 m

Breadth = 3x = 3 × 2 = 6 m

Height = 2x = 2 × 2 = 4 m

Now,

The volume of the cuboid is,

= length × breadth × height

= 10 × 6 × 4

= 240 m²

Thus, the volume of the cuboid is → 240 m².

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