Answer each question. If the lengths of the sides of a cube ar...

Question

Answer each question. If the lengths of the sides of a cube are tripled, by what factor will the volume change?

Accepted Answer

Hello. Everyone in this video, we're going to be looking at this practice problem where we want to determine the change in the area of a rectangle. If the width is increased by five times and the link is increased by seven times. So first let's get started with what the area of a rectangle is. It should be be with times the length. So in this case all represent the area with a, the, with with W. And the length with L. So normally area is just equal to W. Times L. But they're changing the with or increasing the with five times. So now I have five W. And they're increasing the link By seven. So this becomes seven L. So I'll say a one or the new length. The new area is equal to five W. Times seven L. The new measurements for with and link. So the new area is equal to w. L. But I want to know how much the area of the new rectangle changed compared to the old rectangle. So you can see that the old area is equal to with times length and with times length also appears in my new area. So I'm going to substitute in W. Times L. With the old eh, So I'll be plugging in the old area in place of the width times the link. So if I do that, I now have that the new area Is equal to 35 times the old area. So that's telling me that The new area is 35 times bigger then the old area. But this becomes our final answer for this problem, and you can see that this aligns with answer choice D. So hopefully this video helped and see you next time.

Answer each question. If the lengths of the sides of a cube are tripled, by what factor will the volume change?

Key Concepts

Volume of a Cube

Scaling Factor

Effect of Dimension Changes on Volume

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