## Excel in math and science

### Master concepts by solving fun, challenging problems.

## It's hard to learn from lectures and videos

### Learn more effectively through short, conceptual quizzes.

## Our wiki is made for math and science

###
Master advanced concepts through explanations,

examples, and problems from the community.

## Used and loved by 4 million people

###
Learn from a vibrant community of students and enthusiasts,

including olympiad champions, researchers, and professionals.

## Comments

Sort by:

TopNewestLet the square base have sides =x and height = h. V=x * x * h. But if paper is L * L, x=L-2h. \(So~~ V=(L^2-4Lh+4h^2) * h.\\\dfrac{dV}{dh}=L^2-8Lh+12h^2=0 ~~~\implies 12h^2-8hL+L^2 \\For~~max~~h=\dfrac{8L-\sqrt{64^2-48L^2}}{24}=\dfrac L 6.~~\implies~ x= L-2*\dfrac L 6=\dfrac {2L}{3}...\large....x=\dfrac {2L}{3} ~~~~h=\dfrac L 6.\) – Niranjan Khanderia · 2 years, 3 months ago

Log in to reply