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  1. #1
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    Math Review Help

    Question 1: Solved

    Find the lateral(side) surface area of the cone generated by revolving the line segment y = x/2, 0<= x <= 4, about the x-axis.

    i got (pi*sqrt5)/2 just like the image however the answer is 4pi*sqrt5

    now when i looked at the image they multiply my answer with

    x^2/2

    my question is how did they get that and why did they multiply it into the answer...



    Question 2: how do i get

    x = y^4/4 + 1/8y^2


    in terms of y =
    and find the derivative of it
    Last edited by Reminisce; January 31st 2010 at 09:08 AM. Reason: update
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  2. #2
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    Quote Originally Posted by Reminisce View Post
    Question:

    Find the lateral(side) surface area of the cone generated by revolving the line segment y = x/2, 0<= x <= 4, about the x-axis.

    i got (pi*sqrt5)/2 just like the image however the answer is 4pi*sqrt5

    now when i looked at the image they multiply my answer with

    x^2/2

    my question is how did they get that and why did they multiply it into the answer...
    \frac{x^2}{2} is the antiderivative of x


    A = 2\pi \int_0^4 \frac{x}{2} \sqrt{1 + \frac{1}{4}} \, dx

    A = \frac{\sqrt{5}}{2} \pi \int_0^4 x \, dx

    A = \frac{\sqrt{5}}{2} \pi \left[\frac{x^2}{2}\right]_0^4

    A = \frac{\sqrt{5}}{2} \pi \left[\frac{4^2}{2} - 0\right] = 4\sqrt{5} \pi
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  3. #3
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    oh my other question then is, for problems like this one do i always have to do that?
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  4. #4
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    Quote Originally Posted by Reminisce View Post
    oh my other question then is, for problems like this one do i always have to do that?
    if you want to determine a surface area of revolution, you do.
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  5. #5
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    Question 2.. how do i get

    x = y^4/4 + 1/8y^2


    in terms of y =
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  6. #6
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    Quote Originally Posted by Reminisce View Post
    Question 2.. how do i get

    x = y^4/4 + 1/8y^2


    in terms of y =
    first of all ...

    is it x = \frac{y^4}{4} + \frac{1}{8y^2}

    or x = \frac{y^4}{4} + \frac{1}{8} y^2

    ?

    second ...

    why do you need to get y in terms of x? what is the context of this problem?
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  7. #7
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    i was looking at the solution manual but it turns out that the manual skip alot the question and didn't fix it... But thanks..
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