## anonymous 3 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. anonymous

Do you know what the volume of a pyramid is?

2. anonymous

1/3 (b)(h)?

3. anonymous

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. anonymous

To find the ratio*

5. anonymous

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

6. anonymous

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

7. anonymous

h=12.

8. anonymous

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

9. anonymous

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. anonymous

So, 20?

11. anonymous

Ratios mean you divide, not multiply.

12. anonymous

Now I'm confused :(

13. anonymous

14. anonymous

I thought you said it was multiplied by 5?

15. anonymous

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

16. anonymous

ratio*

17. anonymous

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

18. anonymous

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

19. anonymous

Allright better explanation.

20. anonymous

It's a 1/5 ratio right?

21. anonymous

Because we scale the pyramid by a factor of 5.

22. anonymous

1:5 ratio sorry.

23. anonymous

Ignore all the other parts.

24. anonymous

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. anonymous

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

26. anonymous

1/5^3

27. anonymous

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

28. anonymous

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. anonymous

Allright.

30. anonymous

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. anonymous

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

32. anonymous

What don't you understand?

33. anonymous

I want to try and help :c .

34. anonymous

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. anonymous

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. anonymous

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

37. anonymous

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

38. anonymous

:)