Bunuel wrote:

A cylinder is placed inside a cube so that it stands upright when the cube rests on one of its faces. If the volume of the cube is 16, what is the maximum possible volume of the cylinder that fits inside the cube as described?

A. 16/π

B. 2π

C. 8

D. 4π

E. 8π

The volume of the cube is 16Volume of cube = (side length)³

So: 16 = (side length)³

So, side length =

∛16So, the BASE of the cube is a SQUARE with dimension

∛16 by

∛16So, the largest cylinder to fit inside the cube must have a diameter of

∛16This means the RADIUS of the cylinder =

∛16/2

Also, since the cube has HEIGHT

∛16, the largest cylinder to fit inside the cube must have a HEIGHT of

∛16What is the maximum possible volume of the cylinder that fits inside the cube as described?Volume = π(radius)²(height)

= π(

∛16/2)²(

∛16)

= π(16/4)

= 4π

= D

Cheers,

Brent

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Brent Hanneson – Founder of gmatprepnow.com