Hoozan wrote:
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?
(A) 20π
(B) 24π
(C) 25π
(D) 96π
(E) 100π
We have three options:
(1) Use 4*5 as the base and 6 as the height
(2) Use 4*6 as the base and 5 as the height
(3) Use 5*6 as the base and 4 as the height.
However, the volume from (2) is strictly less than that of (1) so we only need to consider (1) and (3).
From (1) we can only use 4*4 of the base, so the radius is 2 and the volume is \(2*2*\pi * 6 = 24\pi\).
From (3) we can only use 5*5 of the base, so the radius is 2.5 and the volume is \(2.5*2.5*\pi*4 = 25\pi\).
Therefore (3) is bigger than we choose C.
Ans: C
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