missashleyn Group Title 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. one year ago one year ago

1. Dido525 Group Title

Do you know what the volume of a pyramid is?

2. missashleyn Group Title

1/3 (b)(h)?

3. Dido525 Group Title

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 Group Title

To find the ratio*

5. missashleyn Group Title

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

6. Dido525 Group Title

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

7. Dido525 Group Title

h=12.

8. Dido525 Group Title

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

9. Dido525 Group Title

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 Group Title

So, 20?

11. Dido525 Group Title

Ratios mean you divide, not multiply.

12. missashleyn Group Title

Now I'm confused :(

13. Dido525 Group Title

14. missashleyn Group Title

I thought you said it was multiplied by 5?

15. Dido525 Group Title

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

16. Dido525 Group Title

ratio*

17. missashleyn Group Title

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

18. Dido525 Group Title

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

19. Dido525 Group Title

Allright better explanation.

20. Dido525 Group Title

It's a 1/5 ratio right?

21. Dido525 Group Title

Because we scale the pyramid by a factor of 5.

22. Dido525 Group Title

1:5 ratio sorry.

23. Dido525 Group Title

Ignore all the other parts.

24. missashleyn Group Title

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 Group Title

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

26. Dido525 Group Title

1/5^3

27. Dido525 Group Title

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

28. missashleyn Group Title

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 Group Title

Allright.

30. Dido525 Group Title

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 Group Title

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

32. Dido525 Group Title

What don't you understand?

33. Dido525 Group Title

I want to try and help :c .

34. missashleyn Group Title

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 Group Title

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 Group Title

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

37. missashleyn Group Title

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

38. dumbcow Group Title

:)