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

## 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)

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