A closed rectangular box with faces parallel to the coordinate planes has one bottom corner at the origin and the opposite top corner in the first octant on the plane 6x + 2y + z = 1. What is the maximum volume of such a box? volume =

Let V denote the volume of the tetrahedron with vertices (7,0,0), (0,6,0), (0,0,10) and (0,0,0). Calculate the volume of the tetrahedron. V=

A gift box is made in the shape of a triangular prism. The triangular end is an equilateral triangle with length x cm and the length of the box is The volume of the box is 300 cm³. r cmX Кx ст у ст х ст (a) Find an expression for y in terms of x. (b) Show that the total surface area A cm?, of the box, is given by 1200v3, v3x? 2 A = (c) Find the value of x that gives the minimum total surface area. Justify your answer.