A solid brass cube is melted and recast as a solid cone of height h and base radius r. If the height of the cube is h, find r in terms of h.
Volume of cube = H. H. H. = H\(^3\)
the volume of a cone is, V=\(\frac{1}{3}\)πr\(^2\)h.
Volume of cube = the volume of a cone
H\(^3\) = \(\frac{1}{3}\)πr\(^2\)h.
\(\frac{3{H}^3}{πh}\) = r\(^2\)
√\(\frac{3{H}^3}{πh}\) = r
h √\(\frac{3H^2}{π}\) = r
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