Bunuel wrote:

The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical cannister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such cannisters that could be used, what is the radius, in inches, of one that has the maximum volume?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 8

Volume of a cylinder: \(pi*r^2*h\)

Radius = \(\frac{Diameter}{2}\)

The maximum diameter of a cylinder that fits inside the rectangular box is restricted to the length and width of the box.

So, if we have a length =8, width = 10 and height = 6, then max. diameter = 8 and radius = 4;

And, the volume of the cylinder: \(pi*4^2*6=pi*96\)

Let's try another, with length =8, width = 6 and height = 10, then max. diameter = 6 and radius = 3;

And, the volume of the cylinder: \(pi*3^2*10=pi*90\)

Largest radius we can have is 4.

(B) is the answer.