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Volume through rotation of 360 Watch

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    y= -5/7x + 60/7

    lower limit = 5

    upper limit = 12

    I use the pi times (integral of y^2 WRS x and substituting upper and lower limits.

    When I try this question, I get the integral of y^2 as 25/147x^3 - 600/98x^2 + 360/49x

    I can tell this is wrong, and when I substitute in the limits, I get a negative number.

    I do not want to use the volume of cone formula

    What mistake am I making if you know and could you post your working out? I already know the answer but not how to get it. It's 175pi/3
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    One of your terms is incorrect.

    We have

    y^2 = \left(\dfrac{60-5x}{7}\right)^2 = \dfrac{3600 - 600x + 25x^2}{49}
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    (Original post by Regret786)
    y= -5/7x + 60/7

    lower limit = 5

    upper limit = 12

    I use the pi times (integral of y^2 WRS x and substituting upper and lower limits.

    When I try this question, I get the integral of y^2 as 25/147x^3 - 600/98x^2 + 360/49x

    I can tell this is wrong, and when I substitute in the limits, I get a negative number.

    I do not want to use the volume of cone formula

    What mistake am I making if you know and could you post your working out? I already know the answer but not how to get it. It's 175pi/3
    Check \left(\frac{60}{7}\right)^2
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    (Original post by Regret786)
    y= -5/7x + 60/7

    lower limit = 5

    upper limit = 12

    I use the pi times (integral of y^2 WRS x and substituting upper and lower limits.

    When I try this question, I get the integral of y^2 as 25/147x^3 - 600/98x^2 + 360/49x

    I can tell this is wrong, and when I substitute in the limits, I get a negative number.

    I do not want to use the volume of cone formula

    What mistake am I making if you know and could you post your working out? I already know the answer but not how to get it. It's 175pi/3
    I suspect your y^2 is wrong because the x term in your integral is.
    You can make your life easier and less prone to errors if you factorise out the 5/7
    This leads to 5/7(-x+12) and then V = pi x integral of [5/7(-x+12)]^2 = 25pi/49 x integral of (-x+12)^2 dx




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    • Thread Starter
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    Yeah I got it now guys, thanks a lot.

    I made a mistake squaring 60/7. I forgetfully wrote 360/49 instead of 3600/49.

    I had been looking for my mistake for quite a while now, can't believe it was something so small.

    Fixing the mistake gives the correct answer.

    Thanks again
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    I am just curious, how can the problem even be solved without the axis of revolution being stated?

    Peace.
 
 
 
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