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The largest possible cube is enclosed in a cylinder whose height is gr

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Bunuel
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The largest possible cube is enclosed in a cylinder whose height is gr [#permalink] New post   12 Sep 2018, 00:22
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The largest possible cube is enclosed in a cylinder whose height is greater than its diameter. What is the volume of the cube?

(1) The base of the cylinder has area 25π
(2) The height of the cylinder is 10.
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A
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Re: The largest possible cube is enclosed in a cylinder whose height is gr [#permalink] New post   12 Sep 2018, 19:41
Only base radius is required to calculate the maximum volume of the cube.
So, A) is the answer.
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Re: The largest possible cube is enclosed in a cylinder whose height is gr [#permalink] New post   12 Sep 2018, 19:48
Bunuel wrote:
The largest possible cube is enclosed in a cylinder whose height is greater than its diameter. What is the volume of the cube?

(1) The base of the cylinder has area 25π
(2) The height of the cylinder is 10.


Hi Bunuel,

Please help in providing OE for this question.
Much Appreciated. !!!
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The largest possible cube is enclosed in a cylinder whose height is gr [#permalink] New post   12 Sep 2018, 21:43
Bunuel wrote:
The largest possible cube is enclosed in a cylinder whose height is greater than its diameter. What is the volume of the cube?

(1) The base of the cylinder has area 25π
(2) The height of the cylinder is 10.


Diameter d> Height h
The largest possible cube shall have each area diagonal = diameter of the cylinder.
S1 - \(\pi r^2\)=25\(\pi\)
r=5. We can find each edge of cube with the help of diagonal.
Sufficient

S2 - h=10; We need to know the radius.
Insufficient.
Answer A.
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Re: The largest possible cube is enclosed in a cylinder whose height is gr [#permalink] New post   10 Mar 2021, 23:00
Tough question. Not sure if my approach is right, but the answer is A.

This is essentially a circle circumscribed by a square.

(1) The base of the cylinder has area 25π
This allows us to determine the diagonal of the square and hence we can also determine the side length of the square (and hence cube)
Sufficient.

(2) The height of the cylinder is 10.
Cannot determine anything about the square side length.
Insufficient.

A.
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Re: The largest possible cube is enclosed in a cylinder whose height is gr [#permalink]
10 Mar 2021, 23:00
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Bunuel
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