Question 196976
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The volume varies jointly as the height and the square of the radius of the base means:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ V = kr^2h]


You are given that the volume is *[tex \LARGE 54\pi] when the height is 8 and the diameter is 9.  The diameter being 9 means that the radius is 4.5, so:



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 54\pi = k\cdot 8 \cdot (4.5)^2]


where *[tex \LARGE k] is the constant of proportionality.  Solve the above equation for *[tex \LARGE k] and replace *[tex \LARGE k] in the first equation with that value.  (Hint:  Leave it in terms of *[tex \LARGE \pi])



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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