A solid metallic hemisphere of radius 6 cm is melted and given the shape of a right circular cone of base radius 4 cm. Determine the height of the cone.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 27 cm
Melting and recasting does not change the amount of metal, so the volume of the cone equals the volume of the hemisphere.
Volume of the hemisphere \(\displaystyle =\frac{2}{3}\pi r^3=\frac{2}{3}\pi\times6^3=144\pi\,\mathrm{cm^3}\)
Volume of the cone \(\displaystyle =\frac{1}{3}\pi R^2h=\frac{1}{3}\pi\times4^2\times h=\frac{16}{3}\pi h\)
\(\displaystyle \frac{16}{3}\pi h=144\pi\), so \(\displaystyle h=\frac{144\times3}{16}=27\,\mathrm{cm}\)