Question

the curved surface area of a solid metallic sphere is cut in in such a way that the curved surface area of the news share is half of that previous one calculate the ratio of the volumes of the portion cut off and the remaining portion of the sphere

Answer 1

Answer:

The answer is 1:1

Step-by-step explanation:

Curved surface area of initial sphere = 4πr2

Curved surface area of new sphere = (1/2) 4πr2 = 2πr2

The other half’s surface area = 2πr2

So, both the parts are hemispheres, with equal curved surface area and same radius.

Curved Surface area of new sphere is half of the curved surface area of previous one. This implies that the sphere is cut into two equal parts and hence the volumes of the two parts after cutoff will be equal too. So, the ratio will be 1:1.

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.