### Video Transcript

Which of the following describes
how the volume of a rectangular prism is affected after doubling all three
dimensions? Is it (A) π sub new is equal to
six times π sub old? (B) π new is equal to π old
squared. (C) π new is equal to two times π
old. (D) π new is equal to four times
π old. Or (E) π new is equal to eight
times π old.

To answer this question, weβll
begin by recalling the formula for the volume of a rectangular prism. The volume π of a rectangular
prism is the product of its length, its width, and its height. So, letβs call the volume of our
original shape π old. Itβs π€πβ. Now, of course, we could do this in
any order. So, we could write ππ€β or any
other combination. Weβre now going to take our
original rectangular prism and double all of its dimensions.

The height of our new shape is two
times β, which is two β. The width is now two times π€. Thatβs two π€. And the length is two times π. Thatβs two π. And so, we can now calculate the
volume of the new shape. Itβs still the product of all of
its dimensions, but this time thatβs two π€ times two π times two β. When we multiply algebraic
expressions, such as this, we begin by multiplying the numbers. And so, two times two times two is
eight. And the new volume is eight
π€πβ.

We now compare the original volume
to the new volume. And since the original volume is
π€πβ and the new volume is eight times this, this must mean that the new volume is
eight times the old volume. The correct answer, therefore, is
(E) π sub new is equal to eight times π sub old.