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akurathi12
GMAT 1: 490 Q47 V13
Posts: 111
31 Dec 2018, 00:34
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
58% (01:54) correct
42%
(02:12)
wrong
based on 79
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What is the maximum possible volume of a cube which can be placed inside a sphere with radius 10 units? (in unit^3)
A. 8000/√3
B. 8000/3√3
C. 8000√3
D. 2400√3
E. 1000
A. 8000/√3
B. 8000/3√3
C. 8000√3
D. 2400√3
E. 1000
31 Dec 2018, 01:29
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For maximum possible volume of a cube which can be placed inside a sphere, the diameter of the sphere must be equal to the diagonal of the sphere.
Let the radius of sphere be r unit and the side of the cube be a unit.
Given that radius r = 10 units
So, diameter = 2x Radius = 20 units = diagonal of cube
We know diagonal of cube = a√3, where a is the length of each side
Hence, a√3 = 20 units, i. e. a = 20/√3 units
We know volume of cube = a^3 = (20/√3)^3 = 8000/3√3 (unit^3)
Hence, the Correct Answer is Option B. 8000/3√3
Let the radius of sphere be r unit and the side of the cube be a unit.
Given that radius r = 10 units
So, diameter = 2x Radius = 20 units = diagonal of cube
We know diagonal of cube = a√3, where a is the length of each side
Hence, a√3 = 20 units, i. e. a = 20/√3 units
We know volume of cube = a^3 = (20/√3)^3 = 8000/3√3 (unit^3)
Hence, the Correct Answer is Option B. 8000/3√3
02 Jan 2019, 05:24
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Solution
Given:
- • Radius of the sphere = 10 units
To find:
- • The maximum possible volume of a cube
Approach and Working:
- • Diagonal of the cube, a√3 = diameter of the sphere, 20
- o Implies, \(a = \frac{20}{√3}\)
• Volume of the cube = \(a^3 = (\frac{20}{√3})^3 = \frac{8000}{3√3}\)
Hence, the correct answer is Option B
