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January 30th, 2007, 02:56 AM   #1
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Right Circular Cone Problem

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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January 30th, 2007, 03:17 AM   #2
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This is a super-easy problem. Since we are told that h=2r,

and we know that: V = (1/3)(pi)(r^2)(h)

We can just substitue 2r for h and go from there:
V = (1/3)(pi)(r^2)(2r)

V = (2/3)(pi)(r^3)
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January 30th, 2007, 11:02 AM   #3
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The wording is fairly typical (though not ideal) and can't really be simplified. It means that you have to obtain a definition of V in terms of r alone, as distinct from in terms of r and h.

Strictly speaking, you should also state what value r may have (in this case, any non-negative real value), since the formal definition of a function includes specifying its domain.
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January 30th, 2007, 01:04 PM   #4
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ok

It is just plug and chug, right?
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