cube slice

[cosmic compass]

just wondering how you solve this problem

[stuck mirage]

Ok just making a general outline to of the solution as i don't have a pen and paper around me rn

The dimensions after the first cut is basically a prism with base square skewed to one side.

The base is 30×30

Height is 30

And the dimension of the rectangle above is 30×15

Now to find the side length of the slanting slope

You can use Pythagoras theorem

30^2 + 15^2= 1125 ig

So the length of the slant line is root(1125) ≈ 33.5

We've the dimensions now comes the actual part

Finding the volume of the prism is quite easy...just divide the prism in two parts one a cuboid of dimensions 30×30×15 and the other a hmm a pastry of dimensions 15×30×33.5(triangle) ×30(height)

Total vol = 13500 + 6750 = 20250

Sooo

From vertex D you're making a cut

One shape will definitely be a pastry another one will be a rectangular prism skewed to one side

And here I need the pen and paper but I can explain the approach

Basically you have all the dimensions for the prism besides the slant line and let that be x

Now the pastry unlike before isn't right angled

Kk no Im going wrong my bad