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.
- r = h
-
r = √\(\frac{3h^2}{π}\)
- r = πh
- r = h √\(\frac{3}{h}\)
The correct answer is: B
Explanation
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