A cube is enclosed in a cylinder, what is the largest possible volume

Question

A cube is enclosed in a cylinder, what is the largest possible volume of the cube?
 
(1) The volume of the cylinder is 100π
(2) The area of the base of the cylinder is 25π

GMATinsight · Answer

Question : what is the largest possible volume of the cube?

Statement 1 : The volume of the cylinder is 100π

Since we have the volume of the cylinder so with same volume many cylinders are possible but in each of them the volumes of cubes will also be different

Only one case will be obtained in which the volume of the cube will be maximum hence this statement is 
SUFFICIENT

Statement 2 : The area of the base of the cylinder is 25π 
Height of the cylinder is unknown which also restricts the biggest possible cube that can be fit into the cylinder hence
NOT SUFFICIENT

Answer: option A

bawarayogi · Answer

We are given that a cube is enclosed in a cylinder nd we need to find out the maximum possible volume of the cube.
The volume of the cube depends on the side of the cube i.e volume = (side)^3 and the side of the cube and enclosure of the cube will depend on the radius and height of the cylinder.

Statement 1: Volume of cylinder = 100 \pi 
 \pi  r^2 h=100 \pi 
r and h unknowkn 
so statement 1 is insufficient

Now Statement 2: Area of base of cylinder =25pie
area of base = pie*r^2
so pie*r^2=25 pie
r^2=25
so r=5 (as r cannot be -5)
But we don't know the height of the cylinder
so Statement 2 is not sufficient

Combining both statement 1 and statement 2 we get r and h so we can know the largest possible volume of cube.
Hence the answer is Option C

AnupamKT · Answer

In statement 1- volume of cylinder is given. With given data, we cannot find radious and height of cylinder which is required to find volume of cone. 
Statement 2 - base area is given so we can get the radious of cone...
So combining both the statements, we will get both radious and height of cone. So C should be the answer.

Posted from my mobile device

Bigpic · Answer

The largest cube inside a cylinder depends on the latter's base radius and height.
Knowing just the base radius or just the height value of the cylinder is insufficient to determine the volume of the cube.

a)  \pi r^2 h = 100 \pi 
Both r and h are unknown. NOT SUFFICIENT

b) \pi r^2 = 25 \pi 
r value is known. But we do not know anything about h. h may be smaller than r \sqrt{2} . Therefore NOT SUFFICIENT.

Combining both a and b, we can know r and h and hence the value of the volume of the cube.
So answer is C

CluelessLearner · Answer

We don't need the height of the cylinder right?
Since there is only one cube enclosed the area of the base of the cylinder will give us the dimensions of the cube.

πr^2=25 
so  r=5

Diameter of circle = Diagonal of the cross section of the cube =  2*5 = 10 
Therefore Volume of Cube =  13.5*13.5*13.5

So the answer should be  B

gmexamtaker1 · Answer

Hi  CluelessLearner  ,

Actually you need the height of the cylinder, because for different values of height you will get different values as possible volume for the cube.

bumpbot · Answer

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A cube is enclosed in a cylinder, what is the largest possible volume

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A cube is enclosed in a cylinder, what is the largest possible volume

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