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.

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$l = 32 c m, b = 28 c m, h = 10 c m$

$l = 36 c m, b = 24 c m, h = 12 c m$

$l = 32 c m, b = 20 c m, h = 14 c m$

$l = 28 c m, b = 18 c m, h = 8 c m$

answer is C.

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Detailed Solution

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

To find: the dimensions of the given chocolate box

Solution:

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

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

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 = $6 x$ = $6 \times 6 = 36 c m$

breadth = $4 x = 4 \times 6 = 24 c m$

height = $2 x = 2 \times 6 = 12 c m$

Hence, the correct option is option C.

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