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TAGS: GRE Instructor Joined: 10 Apr 2015
Posts: 3907
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What is the volume of the largest cube that can fit [#permalink]
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Expert's post 00:00

Question Stats: 43% (01:58) correct 56% (00:58) wrong based on 32 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  Moderator  Joined: 07 Jan 2018
Posts: 697
Followers: 11

Kudos [?]: 785  , given: 88

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

Posted from my mobile device  GRE Instructor Joined: 10 Apr 2015
Posts: 3907
Followers: 163

Kudos [?]: 4766  , given: 70

Re: What is the volume of the largest cube that can fit [#permalink]
2
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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  Moderator  Joined: 07 Jan 2018
Posts: 697
Followers: 11

Kudos [?]: 785  , given: 88

Re: What is the volume of the largest cube that can fit [#permalink]
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?
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Re: What is the volume of the largest cube that can fit [#permalink]
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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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