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# Volume of a cuboid is given by the product of its length, breadth and height. The length is $2{x^2}$ times its breadth. The height is $\dfrac{3}{2}xy$ times of length. Find volume of cuboid if its breadth is $6{y^2}$.

Last updated date: 17th Jun 2024
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Hint:
This is a volume related problem. We are given a cuboid with its dimensions in the form of x and y with relations between the length, breadth and height. We are going to use the formula we generally use to find the volume of cuboid.
Volume of cuboid= $length \times breadth \times height \Rightarrow lbh$

Complete step by step solution:
Given that a cuboid has,
$breadth(b) = 6{y^2}$
$length(l) = 2{x^2} \times breadth = 2{x^2} \times 6{y^2} = 12{x^2}{y^2}$
$height(h) = \dfrac{3}{2}xy \times length = \dfrac{3}{2}xy \times 12{x^2}{y^2} = 18{x^3}{y^3}$
Now we have all the dimensions with us. Let’s find the volume.
Volume of cuboid= $length \times breadth \times height \Rightarrow lbh$
Putting the values we get
$\Rightarrow 12{x^2}{y^2} \times 6{y^2} \times 18{x^3}{y^3}$
Now taking constant terms on one side
$\Rightarrow 12 \times 6 \times 18 \times {x^2}{y^2} \times {y^2} \times {x^3}{y^3}$
$\Rightarrow 1296{x^{2 + 3}}{y^{2 + 2 + 3}} \to \left( {{a^m}{a^n} = {a^{m + n}}} \right) \\ \Rightarrow 1296{x^5}{y^7} \\$

Thus this is the volume of the cuboid $\Rightarrow 1296{x^5}{y^7}$.

Note:
In this problem we may lose the marks just because we have not added the powers of the same base variables like x and y here. Don’t miss that step. Also use the relations given between the dimensions.
Also by mistake we directly take the value of length as $2{x^2}$ whereas it is $2{x^2}$ times the breadth. Same for height also. So be attentive.