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\noindent {\bf Problem statement} A sort of raindrop is obtained by
revolving the profile curve

$$y=\sqrt{x}(x-C)^2 \ {\rm for} \ 0\le x \le C$$

about the $x$-axis. Here $C$ is a positive constant.

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\noindent a) Sketch the profile curve and the solid of revolution.

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\noindent b) For which value of $C$ will the raindrop have volume 1?
What are the approximate dimensions (length and diameter) of this
raindrop?

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