# How do you find the volume of the solid bounded by the coordinate planes and the plane #7x+y+z=4#?

the drawing is key. start by finding the intercepts with each of the axes, the intercept line on the xy plane follows as

the volume is simply

it can be done as

OR

in each case comes out at

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To find the volume of the solid bounded by the coordinate planes and the plane (7x+y+z=4), you can set up a triple integral over the region enclosed by the planes. Since the solid is bounded by the coordinate planes, its volume can be determined by integrating the constant function 1 over this region. The limits of integration for (x), (y), and (z) will depend on the intersection points of the given plane with the coordinate planes. You would integrate 1 with respect to (x), (y), and (z) over these limits to find the volume.

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