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8867564

  • 3 years ago

1) Find the volume of the solid of revolution formed when the region bounded between x = 1, x = 4, y = x2 and y = 0 is revolved vertically around the x-axis. Using cans is the answer 21π?

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  1. timo86m
    • 3 years ago
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    by x2 you mean x*2 or x^2

  2. timo86m
    • 3 years ago
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    if x*2

  3. timo86m
    • 3 years ago
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    |dw:1337145858842:dw| I think

  4. timo86m
    • 3 years ago
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    area of a small slice will result in a ring so it be pi r2^2 pi r1^2

  5. colorful
    • 3 years ago
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    I know it as shell method never heard "cans" befor lol

  6. colorful
    • 3 years ago
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    |dw:1337146309981:dw|we need the height and radius of each cylinder...

  7. colorful
    • 3 years ago
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    |dw:1337146393852:dw|

  8. colorful
    • 3 years ago
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    the surface area of a cylinder is given by\[2\pi rh\]so in this case each surface area as a function of x is\[A(x)=2\pi rh=2\pi x^2\cdot x=2\pi x^3\]

  9. colorful
    • 3 years ago
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    adding up all these areas from x=1 to x=4 should give us the correct integral

  10. colorful
    • 3 years ago
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    \[V=2\pi\int_{1}^{4}x^3dx\]

  11. 8867564
    • 3 years ago
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    Thank you for the help on this problem. It was very helpful.

  12. timo86m
    • 3 years ago
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    deos y=x^2 or x*2?

  13. 8867564
    • 3 years ago
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    It's x^2

  14. timo86m
    • 3 years ago
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    oh

  15. timo86m
    • 3 years ago
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    you can take area from y=0 to y=1 use pi*4^2-pi*1^2=15 pi so that is first part

  16. timo86m
    • 3 years ago
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    now for 1 to 16 integral(pi*4^2-pi(sqrt(y))^2dy) from 1 to 16

  17. timo86m
    • 3 years ago
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    I got 127.5000000*Pi

  18. timo86m
    • 3 years ago
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    let me know what the answer was :)

  19. marco26
    • 3 years ago
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    what is the answer?

  20. timo86m
    • 3 years ago
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    I got 127.50*Pi

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