# Ex.9.2 Q4 Algebraic Expressions and Identities - NCERT Maths Class 8

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## Question

Obtain the volume of rectangular boxes with the following length, breadth and height respectively.

(i) $$\quad 5a,\,3{a^2},\,7{a^4}$$

(ii) $$\quad 2p,4q,8r$$

(iii) $$\quad xy,\,2{x^2}y,\,2x{y^2}$$

(iv) $$\quad a,\,2b,\,3c$$

## Text Solution

What is known?

Length, breadth and height respectively of rectangular boxes

What is unknown?

Volume of rectangular boxes

Reasoning:

Volume of a Rectangular Box

$$=$$  Length $$\times$$  Breadth $$\times$$ Height

Steps:

We know that,

Volume of a Rectangular Box

$$=$$  Length $$\times$$  Breadth $$\times$$ Height

(i)

\begin{align}& {\rm{Volume }} \\&= 5a \times 3{a^2} \times 7{a^4} \\&= 5 \times 3 \times 7 \times a \times {a^2} \times {a^4} \\&= 105{a^7}\end{align}

(ii)

\begin{align}& {\rm{Volume }} \\ &= 2p \times 4q \times 8r \\ &= 2 \times 4 \times 8 \times p \times q \times r \\ &= 64pqr\end{align}

(iii)

\begin{align} &{\rm{ Volume }}\\& = xy \times 2{x^2}y \times 2x{y^2}\\ & = 2 \times 2 \times xy \times {x^2}y \times x{y^2} \\&= 4{x^4}{y^4}\end{align}

(iv)

\begin{align}& {\rm{Volume }} \\ &= a \times 2b \times 3c \\ &= 2 \times 3 \times a \times b \times c \\&= 6abc\end{align}

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