# Question Video: Writing the Relation between Two Quantities for the Volume of Rectangular Prisms

Which of the following describes how the volume of a rectangular prism is affected after doubling all three dimensions? [A] π_new = 6π_old [B] π_new = πΒ²_old [C] π_new = 2π_old [D] π_new = 4π_old [E] π_new = 8π_old

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### 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, weβll 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, letβs call the volume of our original shape π old. Itβs π€πβ. Now, of course, we could do this in any order. So, we could write ππ€β or any other combination. Weβre 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€. Thatβs two π€. And the length is two times π. Thatβs two π. And so, we can now calculate the volume of the new shape. Itβs still the product of all of its dimensions, but this time thatβs 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€πβ.

We now compare the original volume to the new volume. And since the original volume is π€πβ 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.