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Volumes of rotation Watch

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    Find the volume of revolutions when the area enclosed by the curves 𝑦 = 2𝑥^2
    and 𝑦 = 𝑥^3 is rotated through 360° about the 𝑦-axis.

    I got 256pi/35 but the markscheme says 16pi/5

    Is the answer wrong or am i making a stupid mistake? If you get a different answer please post your method
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    (Original post by stolenuniverse)
    Find the volume of revolutions when the area enclosed by the curves 𝑦 = 2𝑥^2
    and 𝑦 = 𝑥^3 is rotated through 360° about the 𝑦-axis.

    I got 256pi/35 but the markscheme says 16pi/5

    Is the answer wrong or am i making a stupid mistake? If you get a different answer please post your method
    Post your working and we'll tell you where you went wrong.
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    (Original post by stolenuniverse)
    Find the volume of revolutions when the area enclosed by the curves 𝑦 = 2𝑥^2
    and 𝑦 = 𝑥^3 is rotated through 360° about the 𝑦-axis.

    I got 256pi/35 but the markscheme says 16pi/5

    Is the answer wrong or am i making a stupid mistake? If you get a different answer please post your method
    I also got the same answer as you -- Please let me know if you find out where you went wrong
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    (Original post by Jasondazza)
    I also got the same answer as you -- Please let me know if you find out where you went wrong
    I'm starting to get the feeling the mark-scheme is wrong.. but i will tell you if it's not

    EDIT: it's the y-axis *facepalm* XD
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    (Original post by RDKGames)
    Post your working and we'll tell you where you went wrong.
    sorry if the photo is bad
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    (Original post by stolenuniverse)
    sorry if the photo is bad
    The question states it is rotated about the y-axis therefore you need to use the formula \displaystyle V=\pi \int_{a}^b x^2 .dy. You've used the one for rotation about the x-axis.
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    You're finding the volume when you rotate around the x-axis, you need the volume when you rotate about the y-axis.
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    (Original post by RDKGames)
    The question states it is rotated about the y-axis therefore you need to use the formula \displaystyle V=\pi \int_{a}^b x^2 .dy. You've used the one for rotation about the x-axis.
    Thank you!!!
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    (Original post by RDKGames)
    The question states it is rotated about the y-axis therefore you need to use the formula \displaystyle V=\pi \int_{a}^b x^2 .dy. You've used the one for rotation about the x-axis.
    You can also use \displaystyle V = 2\pi \int_0^2 x y \, dx (where here y should be the difference between the 2 curves) which avoids needing to rewrite the original expressions to get x as a function of y.
 
 
 
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