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?
This is a very basic OG question.
The official answer is B because the cylinder of maximum volume that can be fit into the box will have to rest on the 8x10 face.
my query is
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.
Does this not imply that the cylinder has to rest on one either the 6X10 or the 6x8 face.
And therefore cannot have a radius greater than 3.
The question asks for cylindrical canister which has the maximum volume ( bigger the radius bigger the volume will be V = pi r^2h)
Radius will be maximum when we the area of the base of the cuboid is maximum, options are 6 x8 , 6 x10 and 8 x 10,
Out of these if we choose first 2 options maximum diameter for the cylinder would be 6 ( or Radius as 3),
Hence the last option 8 x10, so the diameter of the cylinder becomes 8 and radius 4
I hope this will help ..!