Question

the ratio of Length breadth and height of a cuboid are in the ratio of 3 ratio 2 ratio 1 if the volume of the cuboid is 3072 cm³ and find the dimension of the cuboid​

Answer 1

Answer :-

• Length of Cuboid = 24 cm
• Breadth of Cuboid = 16 cm
• Height of Cuboid = 8 cm

Given :-

• Volume of Cuboid = 3072 cm³

To Find :-

• Length of Cuboid = ?
• Breadth of Cuboid = ?
• Height of Cuboid = ?

Explanation :-

Let the Dimensions of the Cuboid to be '3x', '2x' and '1x' cm.

As we Know,

$\blue { \underline { \boxed { \bf \implies Volume \: of \: Cuboid = L \times B \times H }}}$

Making an Equation,

$\rm : \longrightarrow L \times B \times H = Volume \: of \: Cuboid$

$\rm : \longrightarrow 3x \times 2x \times 1x = 3072 \; \; cm^3$

$\rm : \longrightarrow 6x^2 \times 1x = 3072 \; \; cm^3$

$\rm : \longrightarrow 6x^3 = 3072 \; \; cm^3$

$\rm : \longrightarrow x^3 = \dfrac{3072}{6} \; \; cm^3$

$\rm : \longrightarrow x^3 = 512 \; \; cm^3$

$\rm : \longrightarrow x = \sqrt[3]{512} \; \; cm^3$

$\red { \underline { \boxed { \bf : \longrightarrow x = 8 \; \; cm }}}$

Now Substituting the values,

$\rm \odot \: Length = 3x = 3(8) = \bold{24 \: cm}$

$\rm \odot \: Breadth= 2x = 2(8) = \bold{16 \: cm}$

$\rm \odot \: Height = 1x = 1(8) = \bold{8 \: cm}$

Hence, the Dimensions of the cuboid are 24 cm x 16 cm x 8 cm.