rahul16singh28 wrote:
pushpitkc wrote:
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
*kudos for all correct solutions
Attachment:
Cylinder_Cube.png
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 \(\frac{4}{\sqrt{2}}\)
For a cube with side \(\frac{4}{\sqrt{2}}\), the volume is \((\frac{4}{\sqrt{2}})^3\) = \((\frac{64}{2\sqrt{2}}) = \frac{32}{\sqrt{2}} = 16\sqrt{2}\)
Therefore, the volume of the largest cube which can fit the cylinder is \(16\sqrt{2}\)
(Option D)Hi
pushpitkcWe know \(a^2 + a^2 = 16.\)
So, \(a^3 = 16\sqrt{2}\)
But why can't the side length be 3. The Diameter of Cylinder is 4. So the cube can be easily fitted with its mid point passing through the centre of circle. Hence, lenght of edge can be 3.
Hi
rahul16singh28,
I will add to what pushpitkc has replied.
When we are imagining about cube with maximum are in a cylinder, we also need to consider how this cube would be inserted in cylinder.
Imagine. You have built cylinder first. Then you have to build a cube and place it inside cylinder.
Now proceed with your calculation.
If you try to insert a cube of side = 3. diagonal of cube becomes \(3\sqrt{2}\).
Note that when we try to insert a square in a circle, we always consider the diagonal of square. Isn't it.
Because diagonal of square will be equal to diameter of circle. And this ensures that square fits in the circle perfectly.
And E is definitely trap answer and most of us would select it, when we are short of time on the exam day.
Hope this will help you to understand how to approach the questions like this.