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.

  • A r = h
  • B r = √\(\frac{3h^2}{Ï€}\)
  • C r = Ï€h
  • D r = h √\(\frac{3}{h}\)
waec 2021mathematics

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

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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