Question

The length and breadth and height of a cuboid are $(x+3),(x-2)$ and $(x-1)$ respectively. Find its volume.

Answer 1

Volume of cuboid is length $\times$ breadth $\times$ height

Here, the length is $(x+3)$, breadth is $(x-2)$ and height is $(x-1)$.

Therefore, the volume of cuboid is:

length$\times$ breadth $\times$ height $=$ $(x+3)(x-2)(x-1)$

Firstly multiply the first and second term as follows:

$(x+3)(x-2)(x-1)=[(x\times x)+(x\times -2)+(3\times x)+(3\times -2)](x-1)$

$=(x^2-2x+3x-6)(x-1)$

$=(x^2+x-6)(x-1)$

Now multiply the resulting expression:

$(x^2+x-6)(x-1)=(x^2\times x)+(x^2\times -1)+(x\times x)+(x\times -1)+(-6\times x)+(-6\times -1)$

$=x^3-x^2+x^2-x-6x+6$

$=x^3-7x+6$

Hence, volume of cuboid id $x^3-7x+6$.