The length, breadth and height of the rectangular box is $3 x y, (4 x^{2} y + 2 x) a n d 2 z$ m respectively. Find the volume of the rectangular box.

(12 x^{3} y^{2} z + 12 x^{2} y z) m^{3}

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(12 x^{3} y^{2} z + 24 x^{2} y z) m^{3} .

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(24 x^{3} y^{2} z + 12 x^{2} y z) m^{3} .

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(24 x^{3} y^{2} z + 24 x^{2} y z) m^{3} .

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Solution

The correct option is C $(24 x^{3} y^{2} z + 12 x^{2} y z) m^{3} .$
Given:
Length $= 3 x y$
Breadth $= 4 x^{2} y + 2 x$ and
Height $= 2 z$ m
Volume of the rectangular box = length $\times$ breadth $\times$ height.
$V = 3 x y \times (4 x^{2} y + 2 x) \times 2 z$
$V = 6 x y z \times (4 x^{2} y + 2 x)$
$V = 6 x y z \times 4 x^{2} y + 6 x y z \times 2 x$
$V = 24 x^{3} y^{2} z + 12 x^{2} y z$

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