## missashleyn 2 years ago Can someone help me please? A wooden pyramid, 12 inches tall, has a square base. A carpenter increases the dimensions of the wooden pyramid by a factor of 5 and makes a larger pyramid with the new dimensions. Describe in complete sentences the ratio of the volumes of the two pyramids.

1. Dido525

Do you know what the volume of a pyramid is?

2. missashleyn

1/3 (b)(h)?

3. Dido525

Yep. So in the first case, what would the volume be? You to to find the ration you divide the new value by the old value right?

4. Dido525

To find the ratio*

5. missashleyn

Well I know the height, but what's the base?

6. Dido525

No need. You got $v=\frac{ 1 }{ 3 }A*h$

7. Dido525

h=12.

8. Dido525

Therefore: $v=\frac{ 1 }{3 } * A *12$ = $V=4A$

9. Dido525

Now we are given the ara of the base was increased by a factor of 5. In other words, it was multiplied by 5.

10. missashleyn

So, 20?

11. Dido525

Ratios mean you divide, not multiply.

12. missashleyn

Now I'm confused :(

13. Dido525

14. missashleyn

I thought you said it was multiplied by 5?

15. Dido525

Haha, yeah for the new volume. But when you find a ration you divide the new value by the old value.

16. Dido525

ratio*

17. missashleyn

So... what is the ratio of the volumes of the 2 pyramids? o.o

18. Dido525

Lol, I don't want to give you an answer :P . I would rather you understand it.

19. Dido525

Allright better explanation.

20. Dido525

It's a 1/5 ratio right?

21. Dido525

Because we scale the pyramid by a factor of 5.

22. Dido525

1:5 ratio sorry.

23. Dido525

Ignore all the other parts.

24. missashleyn

I'm seriously so confused it's not even funny! Lol okay so the dimensions are increased by a facor of 5. So you're saying the ratio of the 2 pyramids is 1:5?

25. Dido525

Ahh but remember, since this is volume, we cube that 5.

26. Dido525

1/5^3

27. Dido525

or 1:125 which can also be 1/125.

28. missashleyn

My head is starting to hurt..so I cube the ratio 1:5? WHAT? Lol you have to break it down for me all at once. I don't do step by step :b

29. Dido525

Allright.

30. Dido525

The scale factor of the Pyramid is 1:5 right? This can be re-written as 1/5 . So the ratio would be 1:5 but since we are dealing with volumes, We have to cube that ratio or in other words, 1/5^3 or 1/125. We can say the New pyramid is 125x more greater than the old pyramid.

31. missashleyn

Is that the answer or are you waiting for me to answer? Lol I don't know how to do this.

32. Dido525

What don't you understand?

33. Dido525

I want to try and help :c .

34. missashleyn

I'm confused on the entire thing lol, I mean I'd like to understand how to get the right answer so I can fully explain my answer in complete sentences but at this point my head is starting to hurt and I just want to finish it. Lol

35. dumbcow

initial dimensions; height = 12 let the square base have dimensions of 1 so initial volume = 4 new dimensions, multiply lengths by 5 height = 60 square base have sides of 5 .... so area of 25 new volume = (1/3)(25)(60) = 500 volume ratio = 500/4 = 125 does that help?

36. dumbcow

in general, the rule is that the volume ratio = (length ratio)^3 --> 5^3 = 125

37. missashleyn

Yes! Thank you both for helping me.. sorry I get confused so easily! I appreciate you both! :)

38. dumbcow

:)