Chapter 4, Problem 5PST

To determine

The factor by which the volume of the prism will increase.

Answer to Problem 5PST

Option C. 27 is correct.

Explanation of Solution

Given:

The given figure is:

  

Calculation:

The volume of original prism is:

  $\begin{array}{l}V=lwh\\ V=6\left(4\right)\left(3\right)\\ V=72\end{array}$

When the dimensions are tripled;

  $l=18\text{ cm , w = 12 cm , h = 9 cm}\text{. }$

Volume of new prism will be:

  $\begin{array}{l}V=lwh\\ V=18\left(12\right)\left(9\right)\\ V=1944\end{array}$

As, $1944=27\left(72\right),$ the volume is increased by 27 times.

So, Option C. 27 is correct.