My Math Forum Right Circular Cone Problem

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 January 30th, 2007, 02:56 AM #1 Senior Member   Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1 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."
 January 30th, 2007, 03:17 AM #2 Senior Member   Joined: Dec 2006 Posts: 1,111 Thanks: 0 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)
 January 30th, 2007, 11:02 AM #3 Global Moderator   Joined: Dec 2006 Posts: 18,956 Thanks: 1602 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.
 January 30th, 2007, 01:04 PM #4 Senior Member   Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1 ok It is just plug and chug, right?

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# if the height h of a right circular cylinder is twice the radius r, express the volume V as a function of r

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