A solid brass cube is melted and recast as a solid cone of height h...
MATHEMATICS
WAEC 2021
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 = √\(\frac{3h^2}{π}\)
- C. r = πh
- D. r = h √\(\frac{3}{h}\)
Correct Answer: B. r = √\(\frac{3h^2}{π}\)
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
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