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Unofficialllyy

  • one year ago

Can someone help with this geometry problem? I will fan and medal!

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  1. Unofficialllyy
    • one year ago
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    The main tank has a radius of 70 feet. What is the volume of the quarter-sphere sized tank? Round your answer to the nearest whole number. You must explain your answer using words, and you must show all work and calculations to receive credit.

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  2. Unofficialllyy
    • one year ago
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    I know I have to use the formula for volume of a sphere which is \[V=\frac{ 4 }{ 3 } \Pi r^3\] Then I plug in 70 to get \[V=\frac{ 4 }{ 3 } \Pi (70)^3\]

  3. Unofficialllyy
    • one year ago
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    Is this correct so far?

  4. Vocaloid
    • one year ago
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    well, yes, you are correct so far V is the volume of the entire sphere, so how do we find the volume of a quarter sphere?

  5. Unofficialllyy
    • one year ago
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    Or would it be \[V=\frac{ 4 }{ 3}(\Pi 70^3)\]

  6. Unofficialllyy
    • one year ago
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    Oh I see. Hang on a sec

  7. Vocaloid
    • one year ago
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    (as a side note, V = (4/3)(pi*70^3) is the same as V = (4/3)(pi)(70^3) because of order of operations)

  8. Unofficialllyy
    • one year ago
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    I'm not sure, when I watched the help video it said to use the formula for the volume of a sphere.

  9. Vocaloid
    • one year ago
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    volume of a quarter-sphere = (1/4)*volume of sphere

  10. Mertsj
    • one year ago
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    Volume of sphere: \[\frac{4}{3}\pi r^3\] Volume of 1 quarter of sphere: \[\frac{1}{4}\times\frac{4}{3}\pi r^3=\frac{1}{3} \pi r^3\]

  11. Unofficialllyy
    • one year ago
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    So I find the volume first then multiply it by 1/4?

  12. Mertsj
    • one year ago
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    yes, that will work. Or as I have shown you could multiply 70^3 by pi and divide by 3

  13. Unofficialllyy
    • one year ago
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    i am stuck on the \[V=\frac{ 4 }{ 3 } \pi (70)^3\] part though. Like how do I go about solving this?

  14. Mertsj
    • one year ago
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    Do you have a calculator?

  15. Unofficialllyy
    • one year ago
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    Yes but I have to show all work.

  16. Mertsj
    • one year ago
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    You have to show the multiplication and division?

  17. Unofficialllyy
    • one year ago
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    I dont think so, just explain what I did. But yes I have a calculator

  18. Mertsj
    • one year ago
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    Then put these steps on your paper: Volume of 1/4 sphere = 1/4 x 4/3 x pi x r^3

  19. Mertsj
    • one year ago
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    Now cancel the fours and substitute 70 for r and write: V = 1/3 x 3.14 x 70x70 x 70

  20. Unofficialllyy
    • one year ago
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    I think I got the answer. Is this right? \[V=359189\]

  21. Unofficialllyy
    • one year ago
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    That is rounded to the nearest whole number

  22. Mertsj
    • one year ago
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    Now do 70 x 70 x 70 on your calculator and write: V = 1/3 x 3.14 x 343,000

  23. Mertsj
    • one year ago
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    Now multiply that by 3.14 and divide by 3 and write: V = 359007 ft^3

  24. Unofficialllyy
    • one year ago
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    Thank you

  25. Mertsj
    • one year ago
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    yw

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