Question

If the volume of the parallelopiped with $a,b,$ and $c$ as coteminous edges is $40$ cubic units, then the volume of the parallelopiped having $b+c,c+a,$ and $a+b$ as coterminous edges in cubic units is

• A. $80$
• B. $120$
• C. $160$
• D. $40$

Answer 1

The correct option is A

$80$

Explanation for the correct option.

Find the volume of the parallelopiped.

It is given that the volume of the parallelopiped with $a,b,$ and $c$ as edges is $40$ cubic units, so $\left[abc\right]=40$.

Now the volume of the parallelopiped having $b+c,c+a,$ and $a+b$ as edges is $\left[b+cc+aa+b\right]$ and its value is given as:

$\begin{array}{rcl}\left[b+cc+aa+b\right]& =& \left[a+bb+cc+a\right]\left[\left[bca\right]=\left[abc\right]\right]\\ & =& 2\left[abc\right]\\ & =& 2\times 40\left[\left[abc\right]=40\right]\\ & =& 80\end{array}$

So the volume of the parallelopiped is $80$ cubic units.

Hence, the correct option is A.