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Floating Ball The polynomial function $$f ( x ) = \frac { \pi } { 3 } x ^ { 3 } - 5 \pi x ^ { 2 } + \frac { 500 \pi d } { 3 }$$
$$\left. \begin{array} { l } { \text { 103. (a) about } 7.13 cm \text { ; The ball floats partly above the } } \\ { \text { surface. (b) The sphere is more dense than water and } } \\ { \text { sinks below the surface. } \quad \text { (c) } 10 cm \text { ; The balloon is } } \\ { \text { submerged with its top even with the surface. } } \end{array} \right.$$