(Solved) A sphere and a hemisphere have the same volume. The ratio of their curved surface areas is?

datha

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11 years ago

A sphere and a hemisphere have the same volume. The ratio of their curved surface areas is?

A sphere and a hemisphere have the same volume. The ratio of their curved surface areas is ?

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dattallmofo_

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11 years ago

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smluke2000

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11 years ago

A sphere and a hemisphere have the same volume.
The ratio of their curved surface areas is?
-----------------------------------------------------------------------

d^2 pi = 1/2 D^2 pi

factor out pi

d^2 = 1/2 D^2

divide both sides by d^2

1 = 1/2 (D^2/d^2)

multiply both sides by 2

2 = (D^2/d^2)

take the square root of both sides

sqrt(2) = D/d

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nursejm

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11 years ago

This verified answer contains over 280 words.

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daTALLsmurf2

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11 years ago

Let R and r be the radius of sphere and hemishpere respectively and S and s be the surface area

Curved surface area of sphere...........S......4?R²
------------------------------------------------ = ---- = --------
Curved surface area of hemisphere....s.....½*4?r²

..S......2R²
---- = --------
..s........r²

Since their volumes are equal we also get ½*(4/3)?r³ = (4/3)?R³
or r³ = 2R³ or r/R = (2)^?
=> Also from r³ = 2R³ we can say 2R²/r² = r/R, which is (2)^?
hence ratio of curved surface area of shere / hemisphere (S/s) = r/R = (2)^? or 1.2566

or surface area of Sphere (S) = (2)^? * surface area of Hemisphere (s) of same volume
or surface area of Sphere (S) = 1.2566 * surface area of Hemisphere (s) of same volume

Hope this helped

Vick

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