A solid hemisphere of radius 24 cm is melted and identical cones each of base radius 8 cm and height 6 cm are formed. How many such cones are formed?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 72
Melting and recasting does not change the amount of metal, so the volume of the hemisphere equals the total volume of the cones.
Volume of the hemisphere \(\displaystyle=\frac{2}{3}\pi r^3=\frac{2}{3}\pi\times24^3=9216\pi\) cm3
Volume of one cone \(\displaystyle=\frac{1}{3}\pi r^2h=\frac{1}{3}\pi\times8^2\times6=128\pi\) cm3
Number of cones \(\displaystyle=\frac{9216\pi}{128\pi}=72\)