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Term Value is defined as the sum of the length of the largest rod wh
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16 Jun 2023, 00:57
16 Jun 2023, 00:57
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Question Stats:
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Term ‘Value’ is defined as the sum of the length of the largest rod which can be placed inside a cube and the radius of the largest possible sphere which can be put in the same cube.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE GEOMETRY
Quantity A |
Quantity B |
The ‘Value’ of cube of side 4 units |
8 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE GEOMETRY
Re: Term Value is defined as the sum of the length of the largest rod wh
[#permalink]
16 Jun 2023, 06:33
16 Jun 2023, 06:33
1
Pythagoras for 3D shapes:
\(a^2+b^2+c^2=z^2\)
Since we have a cube, a=b=c=4
The longest rod that can be placed in the cube is therefore:
\(4^2+4^2+4^2=z^2\)
\(4^2*3=z^2\)
\(4*3=12=z\)
We can stop here.
The largest rod in a sphere must be some positive value - there cannot be a negative length.
As QB is 8, the largest rod in the cube already makes QA larger than QB.
A.
\(a^2+b^2+c^2=z^2\)
Since we have a cube, a=b=c=4
The longest rod that can be placed in the cube is therefore:
\(4^2+4^2+4^2=z^2\)
\(4^2*3=z^2\)
\(4*3=12=z\)
We can stop here.
The largest rod in a sphere must be some positive value - there cannot be a negative length.
As QB is 8, the largest rod in the cube already makes QA larger than QB.
A.
Re: Term Value is defined as the sum of the length of the largest rod wh
[#permalink]
16 Jun 2023, 20:54
16 Jun 2023, 20:54
1
Rod length = Diagonal of cube = 4rt3
Radius of sphere = side of cube/2 = 2
Total = 4rt3 + 2 > 8
Radius of sphere = side of cube/2 = 2
Total = 4rt3 + 2 > 8
