# Thread: Real life geometry problem

1. ## Real life geometry problem

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

2. 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 $A(x,y) = 2xy$ and $r^2 = x^2+y^2$ then $A(x) = 2x\times \sqrt{14.5^2-x^2}$ now find $x$ where $A'(x)=0$

After you have this we can find the third deminsion.

3. Originally 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 $A(x,y) = 2xy$ and $r^2 = x^2+y^2$ then $A(x) = 2x\times \sqrt{14.5^2-x^2}$ now find $x$ where $A'(x)=0$

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 problem