A tank obliquely cut (part 2)
Before trying this problem, you need to solve
A tank obliquely cut
.
The top part of a tank that originally had a cuboid shape has been cut by a plane not parallel to its horizontal base, as seen in the picture. What is the maximum volume of liquid the tank can hold, in a convenient way? The lengths of some edges are given in the picture:
- dimensions of rectangular base: length 5 , width 2
- lengths of vertical edges (only three of them are known): 4 , 6 and 7
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In order for the tank to hold as much liquid as possible, we must tilt it so that its oblique (yellow) face becomes horizontal. In this case, the volume of the liquid equals the volume of the tank. Let’s calculate this:
As we know from A tank obliquely cut , the length of the green edge is 3.
The minimum height the cuboid could have before it was cut is 7 (shape A) and it can be considered as a compound of two other cuboids (shapes B and C). In turn, shape B consists of shapes D and E, which are enantiomorphs , (i.e. mirror images of each other) thus they have the same volume.
Consequently, we have:
V max = V t a n k = V C + V E = V C + 2 V B = ( 2 × 5 × 3 ) + 2 1 ⋅ ( 2 × 5 × 4 ) = 5 0