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 √\(\frac{3}{h}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Volume of cube = H. H. H. = H\(^3\)
the volume of a cone is, V=\(\frac{1}{3}\)\pir\(^2\)h.
Volume of cube = the volume of a cone
H\(^3\) = \(\frac{1}{3}\)\pir\(^2\)h.
\(\frac{3{H}^3}{\pih}\) = r\(^2\)
\sqrt\(\frac{3{H}^3}{\pih}\) = r
h \sqrt\(\frac{3H^2}{\pi}\) = r
Source: WAEC / JAMB / NECO Classroom Archive (Record #61299)