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 ?

Answer 1

Given :- 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 ?

Solution :-

we know that,

• when a cone of maximum possible volume is cut off from a solid metallic right circular cylinder or radius r and height as h , then = radius of cone is equal to radius of cylinder , and also, height of cone is equal to height of cylinder.

So,

→ Volume of cylinder = V = πr²h

then,

→ Volume of cone = (1/3)πr²h = (1/3)V = (V/3)

Now,

→ Remaining metal of cylinder = V - (V/3) = (2V/3) .

Now, given that, this remaining metal is melt and recast into four identical solid spheres.

So,

→ 4 * (Volume of sphere) = (2V/3)

→ Volume of sphere = (2V/3) * (1/4)

→ Volume of sphere = (V/6) (Ans.)

Hence, Volume of Each sphere is (V/6) .

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