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# What is the volume of the largest cube that can fit

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GRE Instructor
Joined: 10 Apr 2015
Posts: 1227
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Kudos [?]: 1105 [1] , given: 7

What is the volume of the largest cube that can fit [#permalink]  02 Jun 2018, 06:55
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Question Stats:

54% (02:05) correct 45% (00:58) wrong based on 11 sessions
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
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Director
Joined: 07 Jan 2018
Posts: 550
Followers: 4

Kudos [?]: 476 [1] , given: 84

Re: What is the volume of the largest cube that can fit [#permalink]  17 Jun 2018, 17:03
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Hello Brent can you put an ans to this question.

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GRE Instructor
Joined: 10 Apr 2015
Posts: 1227
Followers: 45

Kudos [?]: 1105 [1] , given: 7

Re: What is the volume of the largest cube that can fit [#permalink]  18 Jun 2018, 06:24
1
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Expert's post
GreenlightTestPrep 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

Let's first inscribe the largest possible square inside the circle

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

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Director
Joined: 07 Jan 2018
Posts: 550
Followers: 4

Kudos [?]: 476 [1] , given: 84

Re: What is the volume of the largest cube that can fit [#permalink]  20 Jun 2018, 03:20
1
KUDOS
GreenlightTestPrep wrote:
GreenlightTestPrep 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

Let's first inscribe the largest possible square inside the circle

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

Cheers,
Brent

Hello Brent, I have a question isn't the volume of a cylinder with r = 2 and height = 3 = $$pi* r^2 * h$$ and in this case $$pi * 2^2 * 3$$ = $$12pi$$ and hence the volume of the cube should be 12pi or closest value less than that and from the option choice E?
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes

GRE Instructor
Joined: 10 Apr 2015
Posts: 1227
Followers: 45

Kudos [?]: 1105 [2] , given: 7

Re: What is the volume of the largest cube that can fit [#permalink]  20 Jun 2018, 05:07
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Expert's post
amorphous wrote:

Hello Brent, I have a question isn't the volume of a cylinder with r = 2 and height = 3 = $$pi* r^2 * h$$ and in this case $$pi * 2^2 * 3$$ = $$12pi$$ and hence the volume of the cube should be 12pi or closest value less than that and from the option choice E?

You're right to say that the correct answer choice be LESS THAN 12pi, but it need not be close to 12pi.

For example, we could have a very wide and very short cylinder with radius 1,000 and height 1. The volume of this cylinder would be HUGE (1,000,000pi to be exact).
However, since we need to place a CUBE inside this cylinder, and since all the sides of a cube must be the same length, the largest possible cube that will fit will be a 1x1x1 cube (with a volume of 1)

So, even though 1 is less than 1,000,000pi, it is not close.

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: What is the volume of the largest cube that can fit   [#permalink] 20 Jun 2018, 05:07
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# What is the volume of the largest cube that can fit

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