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Math Help - Right Circular Cone Volume

  1. #1
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    Right Circular Cone Volume

    The volume V of a right circular cone is V = (1/3)(pi)(r^2)(h). If the height is TWICE the radius, express the volume V as a function of r.

    NOTE: What is a more simple way to say:

    "...express the volume V as a function of r."
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  2. #2
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    Quote Originally Posted by symmetry View Post
    The volume V of a right circular cone is V = (1/3)(pi)(r^2)(h). If the height is TWICE the radius, express the volume V as a function of r.

    NOTE: What is a more simple way to say:

    "...express the volume V as a function of r."
    Hello,

    you've got 2 functions which should be composed:

    h(r)=2r according to your problem

    V = \frac{1}{3} \pi \cdot r^2 \cdot (h). Plug in the term for h:

    V = \frac{1}{3} \pi \cdot r^2 \cdot (2r)= \frac{2}{3} \pi \cdot r^3

    EB
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  3. #3
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    ok

    Understood but tell me, what is a more simple way to say:

    "...express the volume V as a function of r"?
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  4. #4
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    Quote Originally Posted by symmetry View Post
    Understood but tell me, what is a more simple way to say:

    "...express the volume V as a function of r"?
    Hello,

    that's a little bit tricky to answer for me.

    In Germany we would say (literally translated of course!): "V of r"

    But most of the time I'm leafing through my dictionary looking for the adequate expression. So don't trust me here.

    EB
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  5. #5
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    ok

    Tell me, are you a math professor?
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  6. #6
    dcline
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    V as a function of r

    "express V as a function of r" pretty much means make an equation with only V on one side of the equals sign, and r as the only variable on the other.

    i.e. V = (2 / 3) * pi * r^3 (functions are usually written "f(r) = (2/3)*pi*r^3")

    but NOT
    V = (1 / 3) * pi * r^2 * h
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