Homework H$15.$A

Given: A "float" is made up of cylinder $(1)$ with a radius $R$ and a length $H,$ and a

hemispherical cap of weight $W$ and radius $R.$ Assume that the weight of cylinder is

negligible compared to the weight of the cap. The float is placed in water with a specific

weight of $g$ in the orientation shown.

Find: Determine the smallest length $H$ for which the float does not sink.

Use the following parameter values in your work: $R=3in,W=15lb$ and $g=62\mathrm{.}4$

$l\frac{b}{f}{t}^3.$