Question

The curved surface of a solid metalic sphere is cut in such a way that the curved sur
area of the new sphere is half of that previous one. Let us calculate the ratio of the volume
to make the two spheres.
of the portion cut off and the remaining portion of the sphere.​

Answer 1

Answer:

hlo....... good morning....to all

Answer 2

Answer:

$\huge\mathfrak\pink{✩Answer☆}$

Let the radius of the old sphere be =R unit

let the radius of the new sphere be =r unit

therefore,curved surface area of the old sphere =4πR²

and the curved surface area of the new sphere =4πr²

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ATP,

4πR²/2=4πr²

or,R²=2r²

or ,R²=√2r²

or,R²=√2r

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now,volume of the old sphere=4/3πr³=4/3(2r)³ cubic unit

volume of the new sphere=4/3πr³

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volume of the remaining sphere =4/3(√2 r)³-4/3 πr³

⠀⠀ ⠀⠀ ⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀ =4/3π³(2√2-1)

therefore,the ratio of the cut off portion and remaining part =4/3πr³:4/3πr³(2√2-1)

=1:2√2-1 (ANS)

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hope this helps you.