geometry-4

[\'manpreet singh]

The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister 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 canisters that could be used, what is the radius, in inches, of the one that has maximum volume?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

[anuprajan5]

There are 3 cases to this

Face 6X8 Height 10 Volume - pi*3^2*10 = 90pi
Face 8X10 Height 6 Volume - pi*4^2*6 = 96pi
Face 6X10 Height 8 Volume - pi*3^2*8 = 72pi


Therefore maximum volume is when area is 96pi and radius is 4.