The length, breadth and height of a chocolate box are in the ratio  6 : 4 : 2. If the volume of the chocolate box is 10,368 cm³, then find the dimensions of the box.

Given : Volume of the box $=10,368 c{m}^3$

To find: the dimensions of the given chocolate box

Solution:

Let us assume $6x, 4x, 2x$ be the length, breadth and height of chocolate box respectively.

Volume of the box $=l\times b\times h$$=$($6x$)($4x$)($2x$)

Given that, volume of box $=10,368 c{m}^3$

$\Rightarrow 48 x^3=10368$

$\Rightarrow x^3=\frac{10368}{48}$

$\Rightarrow x^3=216$

$\Rightarrow x=\sqrt[3]{216} =6$

Therefore, length  = $6x$ = $6\times 6=36 cm$

                  breadth = $4x=4\times 6=24 cm$

                   height  = $2x=2\times 6=12 cm$

Hence, the correct option is option C.