Sketch and find the volume of the solid bounded by the plane

Solution

answer: say, first choose any x between 0 and 3 (since all are non negative). Then, for given x, y is between 0 and 3-x, and for given x and y, z is between 0 and 3-x-y (as you said). But to get the volume of a pyramid-like solid, you can use Vol = (base area) x height / 3 here the height is 3, and the base is the triangle which is half the square 3x3 (cut by diagonal) i.e. Vol = (3 x 3 / 2) x 3 / 3 =3 x 3 / 2 = 9 / 2 = 4.5