What is the volume of the largest cube that can fit inside a cylinder with radius 2 and height 3?
A) 9
B) 8√2
C) 16
D) 16√2
E) 27
Answer: D
Difficulty level: 650 - 700
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What is the volume of the largest cube that can
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Brent@GMATPrepNow
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If the radius of the cylinder is 2, the diagonal of the bottom face of the cube is 4.
If the length of the diagonal is 4, the side of the cube is 4/(sqrt(2)).
For a cube with side 4/(sqrt(2)), the volume is (4/(sqrt(2)))^3 = 64/(2 srqt(2)) = 32/sqrt(2) = 16*sqrt(2).
Therefore, the volume of the largest cube which can fit the cylinder is 16*sqrt(2), option D.
Regards!
If the length of the diagonal is 4, the side of the cube is 4/(sqrt(2)).
For a cube with side 4/(sqrt(2)), the volume is (4/(sqrt(2)))^3 = 64/(2 srqt(2)) = 32/sqrt(2) = 16*sqrt(2).
Therefore, the volume of the largest cube which can fit the cylinder is 16*sqrt(2), option D.
Regards!
GMAT/MBA Expert
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Brent@GMATPrepNow
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Let's first inscribe the largest possible square inside the circleBrent@GMATPrepNow wrote:What is the volume of the largest cube that can fit inside a cylinder with radius 2 and height 3?
A) 9
B) 8√2
C) 16
D) 16√2
E) 27
Answer: D
Difficulty level: 650 - 700
Source: www.gmatprepnow.com
Since the radius of the cylinder is 2, we know that the DIAMETER = 4
Since we have a RIGHT TRIANGLE, we can apply the Pythagorean Theorem to get: x² + x² = 4²
Simplify: 2x² = 16
So, x² = 8, which means x = √8 = 2√2
ASIDE: On test day, you should know the following approximations:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2
So, we get: x = 2√2 ≈ 2(1.4) ≈ 2.8
At this point, we should recognize that, since the height of the cylinder is 3...
...then the LARGEST CUBE will have dimensions 2√2 by 2√2 by 2√2
Volume = (2√2)(2√2)(2√2)
= 8√8
= 8(2√2)
= 16√2
Answer: D
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
