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Thread: cylinder

  1. #1
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    cylinder

    Any tips?

    Let r be a positive constant. Consider the cylinder x^2 + y^2 \leq r^2, and let C be the part of the cylinder that satisfies
    0 \leq z \leq y .

    a) Consider the cross section of C by the plane x = t ( -r \leq t \leq r .), and express its area in terms of r,t.

    b) Calculate the volume of C, and express it in terms of r.

    c) Let a be the length of the arc along the base circle of C from the point (r,0,0) to the point ( rcos \theta, rsin \theta, 0) 0 \leq \theta \leq \pi .
    Let b be the length of the line segment from the point ( rcos \theta, rsin \theta, 0) to the point  (rcos \theta, rsin \theta, rsin \theta). . Express a and b in terms of r, \theta. .

    d) Calculate the area of the side of C with x^2 + y^2 = r^2, and express it in terms of r.
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  2. #2
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    Re: cylinder

    Can someone relocate to the topic calculus?
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  3. #3
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    Re: cylinder

    Quote Originally Posted by provasanteriores View Post
    Can someone relocate to the topic calculus?
    I presume you are in a Calc class, but the topic is Geometry so it's in the right place.

    -Dan
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  4. #4
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    Re: cylinder

    I found the area = h/4 ??
    The answer is (r - t)/2
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  5. #5
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    Re: cylinder

    the are is (2sqrt(r-t).(sqrt(r-t)/4 = (r-t)/2 ?
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  6. #6
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    Re: cylinder

    Quote Originally Posted by provasanteriores View Post
    Any tips?

    Let r be a positive constant. Consider the cylinder x^2 + y^2 \leq r^2, and let C be the part of the cylinder that satisfies
    0 \leq z \leq y .

    a) Consider the cross section of C by the plane x = t ( -r \leq t \leq r .), and express its area in terms of r,t.

    b) Calculate the volume of C, and express it in terms of r.

    c) Let a be the length of the arc along the base circle of C from the point (r,0,0) to the point ( rcos \theta, rsin \theta, 0) 0 \leq \theta \leq \pi .
    Let b be the length of the line segment from the point ( rcos \theta, rsin \theta, 0) to the point  (rcos \theta, rsin \theta, rsin \theta). . Express a and b in terms of r, \theta. .

    d) Calculate the area of the side of C with x^2 + y^2 = r^2, and express it in terms of r.
    Some letter c?
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