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anonymous

  • one year ago

A cylindrical vase has a diameter of 4 inches. At the bottom of the vase, there are 6 marbles, each of diameter 2 inch. The vase is filled with water up to a height of 8 inches. What is the volume of water in the vase?

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  1. anonymous
    • one year ago
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    26π in3 16π in3 24π in3 32π in3

  2. Valpey
    • one year ago
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    You need to solve for the total volume of the cylinder, then subtract the total volume of the marbles to get the total volume of the water.

  3. Valpey
    • one year ago
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    The volume of a cylinder is \(\pi r^2 h\) (r, the radius is half the diameter) The volume of a sphere is \(\frac{4}{3}\pi r^3\)

  4. anonymous
    • one year ago
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    oh ok

  5. Valpey
    • one year ago
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    What is the volume of the cylinder in terms of \(\pi\)?

  6. anonymous
    • one year ago
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    well pie is 3.14 right?

  7. Valpey
    • one year ago
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    It isn't necessary to use the numerical value of pi. You can leave everything in terms of pi. As in \(x = 15\pi\) or \(y = \frac{2}{3}\pi\).

  8. anonymous
    • one year ago
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    oh ok well idk what the radius is but they tell us the height

  9. Valpey
    • one year ago
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    The radius is half the diameter by definition.

  10. anonymous
    • one year ago
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    oh ok so the radius would be 2?

  11. Valpey
    • one year ago
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    Yes, the radius of the cylinder is 2.

  12. anonymous
    • one year ago
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    ok so it would be π2^2*8

  13. Valpey
    • one year ago
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    Yes, what is that equal to?

  14. anonymous
    • one year ago
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    315.5072?

  15. anonymous
    • one year ago
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    @Valpey

  16. Valpey
    • one year ago
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    Not quite. Let's still leave it in terms of pi. Let's just resolve \(2^2 * 8\).

  17. Valpey
    • one year ago
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    I think you did \((\pi*2)^2 * 8\) when you meant to do \(\pi*(2)^2 * 8\). Still, we don't actually need to multiply by pi.

  18. anonymous
    • one year ago
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    oh ok 2^2*8 is 32

  19. anonymous
    • one year ago
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    and yeah thats what i did

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