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Math Help - More expanding and simplifying and finding volume

  1. #1
    Senior Member Mukilab's Avatar
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    More expanding and simplifying and finding volume

    1)Expand and simplify
    n^2+(n-1)^2 I got n^4-2n+1????

    If n is a whole number show that this expression must be an odd number. From my previous post would this be the answer: (3n)(76)


    2)The radius of a sphere is 3y cm
    The radius of a cylinder is 2y cm and the cylinder's height is H cm
    The volume of the sphere is equal to the volume of the cylinder
    Express the Height (H) of the cylinder in terms of y. Write in the simplest form. No idea how to do this. Please show me a method
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  2. #2
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    1. n^2+(n-1)^2 = n^2 + n^2 - 2n +1 = 2n^2 - 2n + 1

    and proving it is an odd number is easy -

    2n^2 is even because of the two in the front
    2n is even because of the two in the front
    and the remaining 1 makes it odd.

    2. volume of sphere = 4/3\pi r^3
    volume of cylinder = \pi r^2H where H is the height.

    comparing the two:
    4/3\pi (3y)^3 = \pi (2y)^2 H
    4/3\pi 27y^3 = \pi 4y^2 H
    H = (4/3) * (27/4) *y
    H = 9y
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  3. #3
    Senior Member Mukilab's Avatar
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    Thank you for this, a very good and clear post. But please could you explain how you got volume of sphere = ?

    I understand everything else including getting the answer at the end
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  4. #4
    Junior Member
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    this formula is the formula for volume of a sphere...

    you should take it "for granted"...

    if you want i can prove it for you here,

    it isn't complicated but i don't think it's required by you...
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  5. #5
    Senior Member Mukilab's Avatar
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    That's ok, google finally bestowed me with such information
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