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What is the volume of the largest cube that can

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What is the volume of the largest cube that can

by Brent@GMATPrepNow » Sat Jun 02, 2018 6:49 am
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
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by swerve » Sat Jun 02, 2018 8:59 am
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.

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by Brent@GMATPrepNow » Mon Jun 18, 2018 6:20 am
Brent@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
Let's first inscribe the largest possible square inside the circle
Image


Since the radius of the cylinder is 2, we know that the DIAMETER = 4
Image

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
Image


At this point, we should recognize that, since the height of the cylinder is 3...
Image
...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
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