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anonymous

  • one year ago

Aran moved a cone-shaped pile of sand that had a height of 6 ft and a radius of 3 ft. He used all of the sand to fill a cylindrical pit with a radius of 6 ft. How high did the sand reach in the pit? Use 3.14 to approximate pi and express your final answer in tenths.

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  1. mathstudent55
    • one year ago
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    You need the formulas for the volumes of a cone and a cylinder.

  2. anonymous
    • one year ago
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    3.14xr^2xh/3

  3. anonymous
    • one year ago
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    and 3.14xr^2xh

  4. mathstudent55
    • one year ago
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    Correct. Here they are written in LaTeX which makes it easier to understand: \(\Large V_{cone} = \dfrac{1}{3} \pi r^2 h\) \(\Large V_{cylinder} = \pi r^2 h\)

  5. mathstudent55
    • one year ago
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    Now compare the formulas. If you have a cone and a cylinder, and they both have the same radius of the base and the same height, how do the volumes compare?

  6. anonymous
    • one year ago
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    We don't know the height of the cylinder...Right/ I really don't understand

  7. mathstudent55
    • one year ago
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    Let me explain better what I was asking above. I'm not talking about your problem now. This is just in general. Let's say you have a cone and a cylinder. The cone and the cylinder have the same radius. The cone and the cylinder have the same height. What will be the difference in their volumes? To answer this question, just look at the formulas for the volumes. What is the only difference you notice between the volume formulas?

  8. anonymous
    • one year ago
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    1/3?

  9. mathstudent55
    • one year ago
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    |dw:1432764194813:dw|

  10. mathstudent55
    • one year ago
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    Exactly. The only difference is the 1/3 in the cone's volume formula. That means for the same height and radius of a cone and a cylinder, the cone's volume is 1/3 the size of the cylinder's volume.

  11. mathstudent55
    • one year ago
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    Ok. Now let's deal with your problem.

  12. mathstudent55
    • one year ago
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    Since you know the formula for the volume of a cone, you can use it to find the volume of the original pile of sand, which is a cone with given radius and height.

  13. anonymous
    • one year ago
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    169.65?

  14. mathstudent55
    • one year ago
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    |dw:1432764569511:dw|

  15. mathstudent55
    • one year ago
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    Great. Now you need the formula for the volume of a cylinder. Write the formula with the info you know, r = 6, leave the height as h, and set it equal to the volume of the cone you just found above. Then solve for h.

  16. anonymous
    • one year ago
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    3.14*6^2*h 3.14*36*h 113.04*h

  17. anonymous
    • one year ago
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    169.65=113.04*h

  18. anonymous
    • one year ago
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    169.65-113.04=56.61=h?

  19. anonymous
    • one year ago
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    Nope it's wrong ummm I don't know...

  20. mathstudent55
    • one year ago
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    Wait. Just one question. In finding the volume of the cone, did you divide by 3 like the formula requires?

  21. mathstudent55
    • one year ago
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    |dw:1432765558766:dw|

  22. anonymous
    • one year ago
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    wait... That's the answer? that doesn't make sense to me at all.. I got 49.2

  23. mathstudent55
    • one year ago
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    No. The drawing above just shows the volume of the cone. I think when you calculated the volume of the cone, you forgot to divide by 3. The volume of the cone is 56.52 ft^3, not 169.56 ft^3

  24. anonymous
    • one year ago
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    oh.. hehe sorry, my mistake...

  25. anonymous
    • one year ago
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    so 56.52=113.04xh?

  26. anonymous
    • one year ago
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    So h=0.5?

  27. anonymous
    • one year ago
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    Actually no.. I'm just confusing myself more and more

  28. mathstudent55
    • one year ago
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    Ok. Now for the volume of the cylinder: |dw:1432766341984:dw|

  29. mathstudent55
    • one year ago
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    Yes, your cylinder volume is correct. Now we equate the two volumes: |dw:1432766436217:dw|

  30. mathstudent55
    • one year ago
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    Your equation is correct. Now you need to solve for h. Since h is being multiplied by 113.04, you need to do the opposite operation, that is, you need to divide both sides by 113.04

  31. mathstudent55
    • one year ago
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    |dw:1432766554551:dw|

  32. mathstudent55
    • one year ago
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    h = 0.5 ft You are correct. Great job!

  33. anonymous
    • one year ago
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    Oh my gosh! Thank you so much.....

  34. anonymous
    • one year ago
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    Can you check this answer though?

  35. anonymous
    • one year ago
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    Remi has two cone-shaped containers with the same diameter. He will place the smaller container inside the larger one. Before he does this, he wants to fill the larger container with water so that it will be completely full but won’t spill when he places the smaller container inside. The diameter of both containers is 12 cm. The height of the smaller container is 6 cm, and the height of the larger container is 18 cm. What volume of water must Remi put in the large container? Use 3.14 to approximate pi and express your final answer in hundredths. 452.16

  36. mathstudent55
    • one year ago
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    The volumes of the containers are: V(large) = 2034.72 cm^3 V(small) = 678.24 cm^3

  37. mathstudent55
    • one year ago
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    The difference between the volumes is: 2034.72 cm^3 - 678.24 cm^3 = 1356.48 cm^3

  38. mathstudent55
    • one year ago
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    How did you get 452.16 cm^3?

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