The volume of this 3D figure is . We look for the maximum value of for . By , we get as an approximate solution and .
According to the referee of the Journal Origami Society of Japan, maximizing the volume of a cup made from a square sheet of paper is a new problem proposed by the authors. Our previous research is presented in .
The origami wrapping problem, which has been studied by some mathematicians, looks for the biggest object that can be wrapped with a sheet of paper. See .
 M. L. Catalano-Johnson and D. Loeb, "Problem 10716: A Cubical Gift," American Mathematical Monthly, 108(1), 2001 pp. 81–82.
 W. Ogasa, T. Inoue, K. Nishimura, T. Nakaoka, D. Ikeda, A. Kanno, S. Nakamura, H. Matsui, T. Yamauchi, S. Utsuki, and R. Miyadera, "The Maximization of a Cup Made from a Square Sheet of Paper," Science of Origami, 1(1), 2011, in Japanese.