What are the dimensions of the largest (volume) rectangular prisim that can fit through the opening and lay flat inside of the rectangular prism pictured?
The opening is a half circle with a radius of 14.5". My free hand 3d circles aren't the greatest
I see this problem in 2 steps.
Firstly a 2D problem looking down onto the top of the box. From here you a maximising a rectangle inside a semi circle.
You need to find the area of this rectangle as a function and solve it when its derivative is equal to zero.
If the rectangle in question has dimensions y and x thenand
then
now find
where
After you have this we can find the third deminsion.
But you are allowed to tilt the smaller prism when inserting it: so no, I don't think a reduction to a 2D problem does the job. At the very least there is a danger that by assuming that the prism will not be tilted when inserting it we will miss the optimal solution to this problemOriginally Posted by pickslides
I see this problem in 2 steps.
Firstly a 2D problem looking down onto the top of the box. From here you a maximising a rectangle inside a semi circle.
You need to find the area of this rectangle as a function and solve it when its derivative is equal to zero.
If the rectangle in question has dimensions y and x then
After you have this we can find the third deminsion.
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