# How do you find the volume of the pyramid bounded by the plane 2x+3y+z=6 and the coordinate plane?

##### 2 Answers

#### Explanation:

the normal vector is

we can re-write the plane as

for

#z= 0, x = 0 implies y = 2# #z= 0, y = 0 implies x = 3#

and

- -

it's this:

the volume we need is

6

#### Explanation:

We are going to be performing a triple integral.

The cartesian coordinate system is the most applicable. The order of integration is not critical. We are going to go z first, y middle, x last.

On the plane

Along

Along

We are finding the volume so