A solid metallic sphere of radius 8 cm is melted and recasted as a cone of height 8 cm. Find the base radius of the cone (in cm).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 16
Melting and recasting changes the shape but not the volume of metal, so the volume of the sphere equals the volume of the cone.
Volume of the sphere = volume of the cone: \(\displaystyle\frac{4}{3}\pi(8)^3=\frac{1}{3}\pi r^2(8)\)
\(4\times512=8r^2\)
\(r^2=256\), so \(r=16\) cm