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A spherical ball was cut into eight equal pieces along the same axis (

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New post 15 Dec 2018, 10:17
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34% (02:07) correct 66% (01:55) wrong based on 56 sessions

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GMATbuster's Weekly Quant Quiz#13 Ques #5


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A spherical ball was cut into eight equal pieces along the same axis (as shown in figure). The total surface area of the eight pieces is how much more, in square units, than the original surface area of the spherical ball? [ The surface area of the sphere = 4ΠR2]
(1) The diameter of the spherical ball = 10 units.
(2) The total surface area of eight halves is 3 times that of the original surface area.

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Re: A spherical ball was cut into eight equal pieces along the same axis (  [#permalink]

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New post 16 Dec 2018, 05:05
Given : A spherical ball was cut into eight equal pieces along the same axis (as shown in figure).

DI Question : The total surface area of the eight pieces is how much more, in square units, than the original surface area of the spherical ball? [ The surface area of the sphere = 4ΠR2]

So, total surface area of one piece = 1/8*(4ΠR^2) + 1/2 ΠR^2 + 1/2 ΠR^2 = 3/2 ΠR^2
Total surface area of 8 pieces = 8 * 3/2 ΠR^2 = 12 ΠR^2
So, total surface area of the eight pieces is more, in square units, than the original surface area of the spherical ball by 12 ΠR^2 - 4 ΠR^2 = 8 ΠR^2.

Statement (1) : The diameter of the spherical ball = 10 units.
Since Diameter is given, hence radius is known. So we can calculate the value.
SUFFICIENT

Statement (2) : The total surface area of eight halves is 3 times that of the original surface area.
This doesn't add any extra information and hence we can't calculate the value.
SUFFICIENT

Answer A

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Re: A spherical ball was cut into eight equal pieces along the same axis (  [#permalink]

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New post 16 Dec 2018, 23:06
ans is A

Total surface area of each piece= 4πr^2/8 + πr^2
So total surface area of eight pieces = 4πr^2+8 πr^2

difference= 8 πr^2
Statement 1 gives r which is sufficient.
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New post 04 Aug 2019, 20:46
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gmatbusters

I am unable to visualize the figure after the cutting.

I can't understand why the surface area of each piece is added with \(\pi\) \(r^2\)

Also, please provide your official explanation if possible
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A spherical ball was cut into eight equal pieces along the same axis (   [#permalink] 04 Aug 2019, 20:46
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