Answer: The new volume will be \(\dfrac{1}{60}\) of the original volume.
Step-by-step explanation: Given that the width of rectangular prism is reduced to one-tenth of its original size, the height is reduced to one-fourth of its original size and the length is reduced to two-third of its original size.
We are to find the change in the volume of the prism.
We know that
the VOLUME of a rectangular prism with width w units, height h units and length l units is given by
\(V=whl.\)
Now, after change in the dimensions as given, the new dimensions of the rectangular prism will be
\(w'=\dfrac{w}{10},~~h'=\dfrac{h}{4},~~l=\dfrac{2l}{3}.\)
Therefore, the new VOLUME of the prism will be
\(V'=w'h'l'=\dfrac{w}{10}\times\dfrac{h}{4}\times\dfrac{2l}{3}=\dfrac{1}{60}\times whl=\dfrac{1}{60}\times V.\)
Thus, the new volume will be \(\dfrac{1}{60}\) of the original volume.
