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Math Help - finding the perimeter and volume using calc

  1. #1
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    finding the perimeter and volume using calc

    ok so i really do not understand what i have to do here and i would love if someone could help me out just a bit:
    i have to find the perimeter and volume of a solid.the base od the solid is the region of the xy-lane bounded by: y=x^2 -2x +2 , y=0, x=0, and x=3.
    the cross section is a semicircle with diameter in the base of the solid.
    does anyone have any idea as to how i should go about doing this?thanks in advance =)
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by michelle91 View Post
    ok so i really do not understand what i have to do here and i would love if someone could help me out just a bit:
    i have to find the perimeter and volume of a solid.the base od the solid is the region of the xy-lane bounded by: y=x^2 -2x +2 , y=0, x=0, and x=3.
    the cross section is a semicircle with diameter in the base of the solid.
    does anyone have any idea as to how i should go about doing this?thanks in advance =)
    For the volume, you want first to find what the radius of your semicircles are, because you want to integrate \frac{\pi r^2}{2}\,dx. We know that r=\frac{1}{2}f(x) (because f(x) is the diameter, so we need to divide by two to get the radius), so we want to integrate \frac{\pi\cdot\frac{1}{4}f^2(x)}{2} over [0,3].

    \frac{\pi}{8}\int_0^3 (x^2-2x+2)^2\,dx

    Multiply it out and integrate. Final answer:
    Spoiler:
    \frac{39\pi}{20}


    And what do you mean by perimeter of a solid. Do you mean surface area or perimeter around the base?
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  3. #3
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    yes for the perimeter i meant to say surface area, sorry..btu as for the volume thank u so very much!!!
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  4. #4
    Senior Member Pinkk's Avatar
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    You would have to integrate the arc length of the semi-circle cross section over [0,3]. The arc length of a semi-circle is half the circumference of a circle, or \frac{\pi d}{2}, and in this case, d=f(x). So the intergral would be:

    \frac{\pi}{2}\int_{0}^{3}x^{2}-2x+2\,\,dx
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