The base of a solid is the region in the first quadrant bounded by the line x=-2y+6 and the coordinate axes. what is the volume of the solid if every cross section perpendicular to the y-axis is a square.

Step-by-step explanation:

For this case we have the following plot on the figure attached.

We know on this case that represent our radius for the square, since we need cross sections perpendicular to the y axis.

We find the intersection points like this:

Since we are assuming squares for the cross sections the area is given by where r = x= -2y+6.

Since our radius is on terms of x we can create a integral with limits on x in order to find the volume, And we can use the following integral in order to find the volume.

On the left part we are using the following property from algebra:

And after do the integral we got this:

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