The inside dimensions of a rectangular wooden box are 4 meters by 5 meters by 6 meters. A cylindrical drum 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 drums that could be used, what is the volume, in cubic meters, of the one that has maximum volume? Options:
A) 20π	B) 24π	C) 25π	D) 96π	E) 100π
You have three options here. Approach is to calculate volumes for all of them and see which one is greatest.   1. Cylinder's base rests on a 4x5 side of the box. So, height becomes 6 and the maximum possible radius becomes 4/2.   So, maximum volume = π.(4/2)^2.6=π24   2. Cylinder's base rests on a 5x6 side of the box. So, height becomes 4 and the maximum possible radius becomes 5/2.   So, maximum volume = π.(5/2)^2.4=π25   3. Cylinder's base rests on a 4x6 side of the box. So, height becomes 5 and the maximum possible radius becomes 4/2.   So, maximum volume = π.(4/2)^2.5=π20   Option 2 gives maximum value and so that should be the answer, π25.   ANSWER:25π
<result>C</result>
The inside dimensions of a rectangular wooden box are 4 meters by 5 meters by 6 meters. A cylindrical drum 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 drums that could be used, what is the volume, in cubic meters, of the one that has maximum volume?