Question

The curved surfacc of a solid metalic sphere is cut in such a way that the area ofthe newsphere is half ofthat previous one. Let us calculate the ratio of tev of the portion cut off and the remaining portion of the sphere. volumes

Answer 1

it is equal to 4:2 bcz volume of spehr = 4/3 πr^3 and himspher = 2/3πr^3.

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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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