Question

A right circular solid cone of maximum possible volume is cut off from a solid metallic right circular cylinder of volume V. The remaining metal is melt and recast into four identical solid spheres. What is the volume of each sphere ? 

(a) \(\frac{V}{12}\)

(b) \(\frac{V}{9}\)

(c) \(\frac{V}{8}\)

(d) \(\frac{V}{6}\)

Answer 1

(d) \(\frac{V}{6}\)

Volume of remaining metal = Volume of cylinder – Volume of cone 

= πr²h – \(\frac13πr^2h=\frac23πr^2h=\frac23V\)

Volume of 4 spheres = \(\frac23\) V 

⇒ Volume of one sphere = \(\frac{\frac23V}{4}=\frac{V}{6}.\)