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anonymous

  • one year ago

Pyramid A is a square pyramid with a base side length of 14 inches and a height of 6 inches. Pyramid B has a volume of 3,136 cubic inches. How many times bigger is the volume of pyramid B than pyramid A? Give your answer as a percent. Provide an explanation and proof for your answer to receive full credit.

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  1. Vocaloid
    • one year ago
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    first step: find the area of the base of pyramid A if the base of pyramid A is a square with sides 14, what is the area of the square?

  2. anonymous
    • one year ago
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    yes

  3. anonymous
    • one year ago
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    how can i find the area

  4. Vocaloid
    • one year ago
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    area = (side length)^2

  5. anonymous
    • one year ago
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    sorry i really need to understand this

  6. anonymous
    • one year ago
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    so it would be side times length squared?

  7. Vocaloid
    • one year ago
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    the problem tells us that side length = 14 area = (side length)^2 find the area

  8. anonymous
    • one year ago
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    ohhhh

  9. anonymous
    • one year ago
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    okay

  10. anonymous
    • one year ago
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    196

  11. anonymous
    • one year ago
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    it would be 196

  12. Vocaloid
    • one year ago
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    right, (but we're not done yet though) this tells us that base = 196 now, we need to find the volume of pyramid A volume = (1/3)(base)(height) = ?

  13. anonymous
    • one year ago
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    that would be 392

  14. Vocaloid
    • one year ago
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    right. now we need to find 100*(volume of pyramid B)/(volume of pyramid A)

  15. anonymous
    • one year ago
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    so i need to multiply all those numbers right?

  16. Vocaloid
    • one year ago
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    / means divide

  17. anonymous
    • one year ago
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    then it would be 122931200 :/

  18. Vocaloid
    • one year ago
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    volume of pyramid B/volume of pyramid A = ?

  19. anonymous
    • one year ago
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    ooops

  20. anonymous
    • one year ago
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    didnt see that

  21. anonymous
    • one year ago
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    ok wait

  22. anonymous
    • one year ago
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    800

  23. Vocaloid
    • one year ago
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    right, 800% that's our final answer

  24. anonymous
    • one year ago
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    thank you so much. i finally get it

  25. anonymous
    • one year ago
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    can you help me with some other questions?

  26. Vocaloid
    • one year ago
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    sure

  27. anonymous
    • one year ago
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    Use the chart below to answer the questions: Country Population (1997 estimate) Area (square km) U.S. 272,648,000 9,364,520 Romania 22,609,000 237,391 Ghana 18,339,000 237,533 Which of these countries has the greatest population density? Which has the least? Provide an explanation and proof for your answer to receive full credit.

  28. Vocaloid
    • one year ago
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    we have three countries, (US, Romania, and Ghana) and the table tells us the population and area of each, right? population density = population/area so, we need three values: A: population of USA/area of USA B: population of Romania/area of Romania C: population of Ghana/area of Ghana can you calculate these three values, please?

  29. anonymous
    • one year ago
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    yes

  30. anonymous
    • one year ago
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    wait

  31. anonymous
    • one year ago
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    US is 29.115

  32. Vocaloid
    • one year ago
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    good, keep going with the other two

  33. anonymous
    • one year ago
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    Romania is 95.239

  34. Vocaloid
    • one year ago
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    good

  35. anonymous
    • one year ago
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    Ghana is 77.206

  36. Vocaloid
    • one year ago
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    right, so Romania has the largest population density and USA has the smallest

  37. anonymous
    • one year ago
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    ahhh thats it?

  38. Vocaloid
    • one year ago
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    yeah

  39. anonymous
    • one year ago
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    thanks. do have time for one more question?

  40. Vocaloid
    • one year ago
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    sure

  41. anonymous
    • one year ago
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    The coordinates A(0, 0), B(0, 3), C(4, 3) and D(4, 0) are graphed and connected together. What 3-dimensional shape will be created when this shape is rotated about the y-axis? Provide an explanation and proof for your answer to receive full credit.

  42. anonymous
    • one year ago
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    you are the best thanks for helping me out

  43. Vocaloid
    • one year ago
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    |dw:1437327503741:dw|

  44. Vocaloid
    • one year ago
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    this gives us a rectangle when we draw out the 4 points, but when we rotate it around the y-axis like so, we get a cylinder|dw:1437327611870:dw|

  45. Vocaloid
    • one year ago
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    |dw:1437327633016:dw| this is kinda hard to explain, but the final answer is a cylinder

  46. anonymous
    • one year ago
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    okay so what formula did you use to rotate around the y axis?

  47. Vocaloid
    • one year ago
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    haha, there isn't a formula for this one, you kinda have to use your imagination

  48. anonymous
    • one year ago
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    :D

  49. Vocaloid
    • one year ago
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    @mathstudent55 maybe you can explain? I'm really bad when it comes to explaining things like this > >

  50. anonymous
    • one year ago
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    than how do i explain

  51. mathstudent55
    • one year ago
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    @Vocaloid Excellent explanations on all three problems!

  52. anonymous
    • one year ago
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    well im glad you helped me.

  53. Vocaloid
    • one year ago
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    thank you, I'm just having a hard time explaining the whole rotating plane thing, how the rectangle becomes a cylinder

  54. anonymous
    • one year ago
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    yes you are really good at explaining

  55. mathstudent55
    • one year ago
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    When a point that is not on the y-axis is rotated about the y-axis, it creates a circle. As you rotate the rectangle about the y-axis, a cylinder with circular bases is created.

  56. Vocaloid
    • one year ago
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    right, thank you, that's the sort of thing they're probably looking for

  57. anonymous
    • one year ago
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    thank you so much mathstudent55 and Vocaloid

  58. anonymous
    • one year ago
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    i appreciate your time and good explanation :)

  59. mathstudent55
    • one year ago
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    You're welcome, but @Vocaloid is the one who deserves the thanks in this post.

  60. anonymous
    • one year ago
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    how do i give you a medal mathstudent55?

  61. mathstudent55
    • one year ago
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    You can only give one medal per post. If you already gave one to Vocaloid, then you can't give me one.

  62. anonymous
    • one year ago
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    ohh sorry.

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