Answer

Verified

447.3k+ views

**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.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which places in India experience sunrise first and class 9 social science CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE