A metallic sphere of radius 8 cm is melted to form a cone with radius same as that of sphere. What is the height of the cone (in cm)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 32
When a solid is melted and recast, its volume does not change, so the volume of the cone equals the volume of the sphere. The cone has the same radius as the sphere, 8 cm.
Volume of cone = volume of sphere: \(\displaystyle\frac{1}{3}\pi r^2h=\frac{4}{3}\pi r^3\)
\(\frac{1}{3}\pi r^2\) cancels from both sides, leaving \(h=4r\)
Height of the cone: \(h=4\times8=32\) cm