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anonymous

  • one year ago

A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 8 marbles, each of diameter 3 inches. The vase is filled with water up to a height of 10 inches. Which of the following could be used to calculate the volume of water in the vase?

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  1. mathstudent55
    • one year ago
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    Are you sure your answers belong to this problem?

  2. anonymous
    • one year ago
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    Oh! oops. π(10in)2(3in) − 1.5(four over threeπ(8in)3) π(3in)2(10in) − 1.5(four over threeπ(8in)3) π(10in)2(3in) − 8(four over threeπ(1.5in)3) π(3in)2(10in) − 8(four over threeπ(1.5in)3)

  3. mathstudent55
    • one year ago
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    |dw:1438032093295:dw|

  4. mathstudent55
    • one year ago
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    Using the height of the water as the height of a cylinder, what is the volume of water if there were no marbles in the cylinder?

  5. anonymous
    • one year ago
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    okay wait im confused

  6. mathstudent55
    • one year ago
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    Let's find the volume of water you can fit in the vase if there are no marbles in it. The vase is a cylinder of diameter 6 inches and height 10 inches. Can you calculate the volume of such a cylinder?

  7. anonymous
    • one year ago
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    282.74

  8. mathstudent55
    • one year ago
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    |dw:1438032432511:dw|

  9. mathstudent55
    • one year ago
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    Correct. Now by putting 10 marbles in the vase, the vase will not be able to hold as much water. The amount of water volume that will be reduced is the same as the combined volume of all the marbles. Each marble is a sphere. What is the volume of a sphere with diameter 3 inches?

  10. anonymous
    • one year ago
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    14.14

  11. mathstudent55
    • one year ago
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    Good. That is 1 marble. There are 8 of them. What is the volume of the 8 marbles?

  12. anonymous
    • one year ago
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    113.12

  13. mathstudent55
    • one year ago
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    Right. Now you subtract 282.74 - 113.12 all in in^3.

  14. anonymous
    • one year ago
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    169.62 ?

  15. mathstudent55
    • one year ago
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    Correct. In your choices you don't see numbers, you see expressions. Which expression in the choices shows what you just did? volume of cylinder - volume of 8 marbles?

  16. mathstudent55
    • one year ago
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    |dw:1438032915804:dw|

  17. anonymous
    • one year ago
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    c?

  18. mathstudent55
    • one year ago
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    |dw:1438032948978:dw|

  19. anonymous
    • one year ago
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    Oh okay so D?

  20. mathstudent55
    • one year ago
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    Look carefully. In choice c., 10 in is squared in the cylinder formula. In the problem, 10 in. is the height. It is the 3 in. radius that is squared.

  21. mathstudent55
    • one year ago
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    Correct. D is the answer. Good job!

  22. anonymous
    • one year ago
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    Wow thank you so much!!!

  23. mathstudent55
    • one year ago
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    You're welcome.

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