Question

g Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x 2y 3z

Answer 1

V = 4/3 units

Explanation:

See attachment for calculation.

Then we substitute for y and z in the rewritten equation

x = 6 - 2y - 3z, where

y = 1

z = 2/3

x = 6 - 2(1) - 3(2/3)

x = 6 - 2 - 2

x = 2

Recall I stated that the volume of a rectangular box is

V = xyz, now we substitute for all the unknown variables.

V = 2 * 1 * 2/3

V = 4/3 units.