Question 857955
x = side length of the square corner piece cut at each of the original rectangle sheet.


Area of the bottom piece becomes {{{highlight_green((30-2x)(90-2x)=1600)}}}
{{{4*4(15-x)(45-x)=4*4*100}}}
{{{(15-x)(45-x)=100}}}
{{{675-60x+x^2=100}}}
{{{x^2-60x+575=0}}}
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discriminant, 3600-4*575=572=2*2*143
{{{x=(60+sqrt(2*2*143))/2}}}
{{{x=(60+2*sqrt(143))/2}}}
{{{highlight(x=30+sqrt(143))}}}


Volume: expect this to be {{{highlight(highlight((30+sqrt(143))*1600))}}}.
That is, the known base area multiplied by the height of x, which we just solved for.