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anonymous

  • one year ago

You are starting a Shaved Ice business and need to decide on a cup.  Your choices are between a cone and a cylindrical shaped cup.  The cone shaped cup has a diameter of 3.25 inches and is 3.75 inches tall.  The cylindrical cup has a diameter of 4 inches and height of 4.75 inches.  The spherical scoop you have chosen has a diameter of 2.75 inches.  Which cup should you choose if you want two scoops of ice to best fit in the cup? 

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  1. anonymous
    • one year ago
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    @Michele_Laino

  2. Michele_Laino
    • one year ago
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    step #1 we have to compute the volume V of the spherical scoop: \[\begin{gathered} V = \frac{{4 \times 3.14}}{3}{r^3} = \frac{{12.56}}{3} \times {1.375^3} = \hfill \\ \hfill \\ = \frac{{12.56}}{3} \times {1.375^3} = ...? \hfill \\ \end{gathered} \]

  3. Michele_Laino
    • one year ago
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    since if the diameter is 2.75 inches, then the radius is: 2.75/2=1.375 inches

  4. anonymous
    • one year ago
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    okay

  5. anonymous
    • one year ago
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    I got 2.374625

  6. Michele_Laino
    • one year ago
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    I got this: \[\Large \begin{gathered} V = \frac{{4 \times 3.14}}{3}{r^3} = \frac{{12.56}}{3} \times {1.375^3} = \hfill \\ \hfill \\ = \frac{{12.56}}{3} \times {1.375^3} = \frac{{12.56}}{3} \times 2.600 = 10.884inche{s^3} \hfill \\ \hfill \\ \end{gathered} \]

  7. Michele_Laino
    • one year ago
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    \[\large \begin{gathered} V = \frac{{4 \times 3.14}}{3}{r^3} = \frac{{12.56}}{3} \times {1.375^3} = \hfill \\ \hfill \\ = \frac{{12.56}}{3} \times {1.375^3} = \frac{{12.56}}{3} \times 2.600 = 10.884inche{s^3} \hfill \\ \hfill \\ \end{gathered} \]

  8. anonymous
    • one year ago
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    now I have to do the same for the cylindrical cup

  9. Michele_Laino
    • one year ago
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    yes!

  10. Michele_Laino
    • one year ago
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    the volume V of the cylindrical cup is: \[\large \begin{gathered} V = 3.14 \times R \times R \times H = \hfill \\ \hfill \\ = 3.14 \times 2 \times 2 \times 4.75 = ...inche{s^3} \hfill \\ \end{gathered} \] since the radius is 4/2=2 inches

  11. Michele_Laino
    • one year ago
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    I have used this approximation: pi = 3.14

  12. Michele_Laino
    • one year ago
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    what do you get?

  13. anonymous
    • one year ago
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    59.66

  14. Michele_Laino
    • one year ago
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    correct!

  15. anonymous
    • one year ago
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    sorry if Im going slow on the questions I writing the answers and work down

  16. Michele_Laino
    • one year ago
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    ok! no worries! :)

  17. anonymous
    • one year ago
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    I have to calculate the scoops

  18. Michele_Laino
    • one year ago
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    we can see that the cylindrical cup is too large since two scoops of ice occupy 10.884*2= 21.768 inches^3

  19. anonymous
    • one year ago
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    okay

  20. anonymous
    • one year ago
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    thank yu for helping me :D

  21. Michele_Laino
    • one year ago
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    :)

  22. Michele_Laino
    • one year ago
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    now we have to compute the volume of the cone shaped cup

  23. anonymous
    • one year ago
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    okay

  24. anonymous
    • one year ago
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    would is be 59.6 and 10.88

  25. Michele_Laino
    • one year ago
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    here is that volume: \[\begin{gathered} V = \frac{1}{3}3.14 \times R \times R \times H = \frac{{3.14 \times 1.625 \times 1.625 \times 3.75}}{3} = \hfill \\ \hfill \\ = \frac{{3.14 \times 1.625 \times 1.625 \times 3.75}}{3} = \frac{{3.14 \times 2.64 \times 3.75}}{3} = ...inche{s^3} \hfill \\ \end{gathered} \]

  26. Michele_Laino
    • one year ago
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    since the radius is: 3.25/2= 1.625 inches

  27. anonymous
    • one year ago
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    okay

  28. Michele_Laino
    • one year ago
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    what do you get?

  29. anonymous
    • one year ago
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    1.625

  30. Michele_Laino
    • one year ago
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    that is the radius, whereas the volume is: \[\begin{gathered} V = \frac{1}{3}3.14 \times R \times R \times H = \frac{{3.14 \times 1.625 \times 1.625 \times 3.75}}{3} = \hfill \\ \hfill \\ = \frac{{3.14 \times 1.625 \times 1.625 \times 3.75}}{3} = \frac{{3.14 \times 2.64 \times 3.75}}{3} = \hfill \\ \hfill \\ = 10.364inche{s^3} \hfill \\ \end{gathered} \]

  31. Michele_Laino
    • one year ago
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    so the cone shaped cup is too small, since it can not contain 2 scoops of ice, therefore we have to choose the cylindrical cup

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