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anonymous

  • one year ago

A cone has a volume of 6 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of? A. 12 in3 B. 18 in3 C. 24 in3 D. 36 in3

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  1. anonymous
    • one year ago
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    @Mertsj

  2. anonymous
    • one year ago
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    @SolomonZelman

  3. Mertsj
    • one year ago
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    Now let's think for a moment. What is the formula for the volume of a cone?

  4. anonymous
    • one year ago
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    1/3 pi(r)^2

  5. Mertsj
    • one year ago
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    Almost.

  6. anonymous
    • one year ago
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    ???

  7. anonymous
    • one year ago
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    \[Vcylinder =πr^2h\]

  8. anonymous
    • one year ago
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    oh "h"!!!!

  9. Mertsj
    • one year ago
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    \[V _{_{c}}=\frac{1}{3}\pi r^2h\]

  10. Mertsj
    • one year ago
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    What is the formula for the volume of a cylinder?

  11. anonymous
    • one year ago
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    pi(r)^2(h)

  12. Mertsj
    • one year ago
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    Yes. How do the volumes compare?

  13. anonymous
    • one year ago
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    The cone has 1/3

  14. Mertsj
    • one year ago
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    Or another way to say that is "the volume of the cylinder is 3 times the volume of the cone."

  15. anonymous
    • one year ago
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    oh ok

  16. Mertsj
    • one year ago
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    Do you understand? Of course the radii and heights must be the same.

  17. anonymous
    • one year ago
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    yes, but I am still confused how to figure out the volume of the cylinder so the cone can fit in it.

  18. anonymous
    • one year ago
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    The question only gives me the volume of the cone, do I just multiply that number by 3? So 6 * 3 = 18?

  19. anonymous
    • one year ago
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    Are you there? @Mertsj

  20. Mertsj
    • one year ago
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    yes and yes

  21. anonymous
    • one year ago
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    ok so 18 is the answer?

  22. anonymous
    • one year ago
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    Can I ask you another question?

  23. Mertsj
    • one year ago
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    yes. The idea is that if you have a cylinder and cone of equal radii and height, then 3 of the cones will fit in the cylinder.

  24. anonymous
    • one year ago
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    ok

  25. anonymous
    • one year ago
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    Hold on one sec, I have one more question

  26. Mertsj
    • one year ago
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    Are you going to post it or am I supposed to guess what it is?

  27. anonymous
    • one year ago
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    Betty closes the nozzle of the funnel and fills it completely with a liquid. She then opens the nozzle. If the liquid drips at the rate of 14 cubic inches per minute, how long will it take for all the liquid in the funnel to pass through the nozzle? (Use π = 3.14.) (1 point) 4.71 minutes 3.14 minutes 14.13 minutes 9.42 minutes

  28. anonymous
    • one year ago
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    How do you upload an image?

  29. Mertsj
    • one year ago
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    We're talking about a cone here so just calculate the volume of the cone in cubic inches.

  30. Mertsj
    • one year ago
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    Divide that answer by 14 and that will be the number of minutes.

  31. anonymous
    • one year ago
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    The image is a conical funnel

  32. Mertsj
    • one year ago
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    Find the volume of the cone.

  33. anonymous
    • one year ago
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    the volume of the cone is 9.42, right?

  34. Mertsj
    • one year ago
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    What is the radius of the cone?

  35. anonymous
    • one year ago
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    3 in

  36. Mertsj
    • one year ago
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    What is the height of the cone?

  37. anonymous
    • one year ago
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    oh wait I forgot to multiply the height!

  38. anonymous
    • one year ago
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    the height is 7 in

  39. anonymous
    • one year ago
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    65.94 is the volume

  40. anonymous
    • one year ago
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    I think the answer is 4.71 correct?

  41. Mertsj
    • one year ago
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    \[V=\frac{1}{3}(3.14)(3^2)(7)=65.94\in^3\]

  42. anonymous
    • one year ago
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    ok that's what I got

  43. Mertsj
    • one year ago
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    \[\frac{65.94}{14}=4.71minutes\]

  44. anonymous
    • one year ago
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    ok thanks!

  45. anonymous
    • one year ago
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    Do you mind helping me with some more? I don't what to keep you though.

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