## gabbyalicorn one year ago The prism has a volume of 60 in3. What would the volume of the prism be if each dimension were tripled?

1. gabbyalicorn
2. gabbyalicorn

@jim_thompson5910

3. Kash_TheSmartGuy

60 x 3 x 3 x 3=1620in3

4. anonymous

@jim_thompson5910

5. gabbyalicorn

I thought 60 x 60 x 60 .3.

6. jim_thompson5910

Kash_TheSmartGuy has the right idea triple each dimension ----> the volume gets multiplied by 3^3 = 27

7. gabbyalicorn

K

8. jim_thompson5910

try it with a 2by3by4 prism then triple each dimension compare the two volumes |dw:1434426114693:dw|

9. gabbyalicorn

|dw:1434426207123:dw|

10. Kash_TheSmartGuy

So that would be 1620in3

11. gabbyalicorn

Hmm, I'm not getting 1620

12. jim_thompson5910

those were just random examples

13. gabbyalicorn

Oh

14. jim_thompson5910

notice how 648/24 = 27

15. jim_thompson5910

and how 3^3 = 3*3*3 = 27

16. jim_thompson5910

|dw:1434426374216:dw|

17. Kash_TheSmartGuy

Yup^^

18. gabbyalicorn

Oh. Kk

19. gabbyalicorn

k so 648 in^3

20. gabbyalicorn

21. jim_thompson5910

648 was from the example I randomly made up

22. jim_thompson5910

to show the connection between the two prisms

23. Kash_TheSmartGuy

no, that was just an example

24. gabbyalicorn

oh, o3o

25. gabbyalicorn

so 60^3 = 216,000

26. jim_thompson5910

the smaller volume is 60 in^3

27. jim_thompson5910

larger volume = 27*(smaller volume) because each side is tripled

28. gabbyalicorn

so 60 x 3 x 27 = 4,860

29. jim_thompson5910

if you quadrupled each side, then larger volume = 64*(smaller volume) the 64 comes from the fact that 4^3 = 64 ---------------------------------- if you multiplied each side by 5, then larger volume = 125*(smaller volume) the 125 comes from the fact that 5^3 = 125 ---------------------------------- if you multiplied each side by 6, then larger volume = 216*(smaller volume) the 216 comes from the fact that 6^3 = 216 ---------------------------------- etc etc

30. jim_thompson5910

`so 60 x 3 x 27 = 4,860` not quite

31. jim_thompson5910

smaller volume = 60 in^3 larger volume = 27*(smaller volume)

32. gabbyalicorn

60 in^3 = 60 x 60 x 60 just double checking

33. Kash_TheSmartGuy

yup

34. gabbyalicorn

so then 60^3 x 27 which is 5,832,00

35. jim_thompson5910

`60 in^3 = 60 x 60 x 60 just double checking` that's false

36. jim_thompson5910

use a calculator to see what 60*60*60 is

37. gabbyalicorn

i got 216000

38. jim_thompson5910

|dw:1434427062119:dw|

39. jim_thompson5910

so because you got 216000, you can see that 60 in^3 is not the same as 60*60*60

40. gabbyalicorn

i was just about to say that XD

41. gabbyalicorn

but then this whole time it wasn't 60^3 it was 60 x 27

42. jim_thompson5910

yeah because 60 is already a volume (not a side length)

43. gabbyalicorn

-3- kay.