Question

Find the volume of the solid lying under the 1. volume =3 cu. units plane
z=6-x-2 y

Answer 1

To find the volume of the solid lying under the plane z=6-x-2y, set up triple integral based on the limits of integration for x, y, and z.

Step-by-step explanation:

To find the volume of the solid lying under the plane z=6-x-2y, we need to determine the limits of integration for x, y, and z.

First, let's rewrite the equation of the plane as x+2y+z=6. This tells us that the solid is bounded by the plane and the coordinate axes.

Since x, y, and z are all positive in this context, the limits of integration for x, y, and z would be: 0 ≤ x ≤ 6, 0 ≤ y ≤ (6-x)/2, and 0 ≤ z ≤ 6-x-2y.

Now, we can find the volume of the solid by evaluating the triple integral: ∫06 ∫0(6-x)/2 ∫06-x-2y 1 dz dy dx.