Video Transcript
Which of the following describes
how the volume of a rectangular prism is affected after doubling all three
dimensions? Is it (A) 𝑉 sub new is equal to
six times 𝑉 sub old? (B) 𝑉 new is equal to 𝑉 old
squared. (C) 𝑉 new is equal to two times 𝑉
old. (D) 𝑉 new is equal to four times
𝑉 old. Or (E) 𝑉 new is equal to eight
times 𝑉 old.
To answer this question, we’ll
begin by recalling the formula for the volume of a rectangular prism. The volume 𝑉 of a rectangular
prism is the product of its length, its width, and its height. So, let’s call the volume of our
original shape 𝑉 old. It’s 𝑤𝑙ℎ. Now, of course, we could do this in
any order. So, we could write 𝑙𝑤ℎ or any
other combination. We’re now going to take our
original rectangular prism and double all of its dimensions.
The height of our new shape is two
times ℎ, which is two ℎ. The width is now two times 𝑤. That’s two 𝑤. And the length is two times 𝑙. That’s two 𝑙. And so, we can now calculate the
volume of the new shape. It’s still the product of all of
its dimensions, but this time that’s two 𝑤 times two 𝑙 times two ℎ. 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
𝑤𝑙ℎ.
We now compare the original volume
to the new volume. And since the original volume is
𝑤𝑙ℎ 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) 𝑉 sub new is equal to eight times 𝑉 sub old.
