Question

I need help with this question, I've tried everything to figure it out. I just don't understand! [picture below!]

Answer 1

As a first step, we can let l, w, and h be the length, width, and height respectively, in centimeters, of the original prism. What two equations can we make using the given info about volume and surface area?

Answer 2

do you mean:
Volume: V=whl
Surface area: SA=2(wl+hl+hw)?

Answer 3

Yes. And you are given both volume and surface area. So \[lwh = 16\] and \[2(wl + hl +hw) = 40.\]

Answer 4

Now we can use the smaller prism to learn how the dimensions are related to one another. For example, how is the width related to the height?

Answer 5

The width and the height are the same.....?

Answer 6

Precisely. So you can now make the substitution \( h=w\) in all the equations. Now similarly, can you relate the length to the width (or the height, whichever you chose to keep in the equations)?

Answer 7

5+5=10, or 5x2= 10

Answer 8

We are determining the ratio of the length to the width, because that doesn't change for similar shapes. The difference varies with the size of the shape. So your second statement is more useful.

Answer 9

What is \(l\) in terms of \(w\)?

Answer 10

um......I don't quite understand what that means.....

Answer 11

What I'm trying to say is: we determined that the width equals the height, so \( h=w\). We also know that the length is double the width, so \(l=2w\).

Now that we know that, can you use these equations to rewrite the volume equation \[lwh=16\] only in terms of \(w\)?

Answer 12

wait I think I might have figured it out, 2x2x4=16?

Answer 13

Yep. Those are the dimensions. Good work!

Answer 14

Thank you so much!