A right circular solid cone of maximum possible volume is cut off from

1.	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» (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 = \(\frac{\frac23V}{4}=\frac{V}{6}.\)

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»

(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 = \(\frac{\frac23V}{4}=\frac{V}{6}.\)