1. ## Volumes by Cross-Sections

A solid has at its base the region bounded by the parabola x-y^2 = -8 and the left branch of the hyperbola x^2-y^2-4=0. The vertical slices perpendicular to the x-axis are squares. Find the volume of the solid. This is the full problem.

I was able to find out the points of intersection, which were x=-3 and x=4. I am not sure what the cross-sectional area is.

2. Originally Posted by dalbir4444
A solid has at its base the region bounded by the parabola x-y^2 = -8and the left branch of the hyperbola x^2-y^2-4=0. The vertical slices perpendicular to the x-axis are squares. Find the volume of the solid.
Could you please post the problem as it is written and show your attempt at the solution?

3. hi dalbir4444,

the left side of the hyperbola is $x=-\sqrt{y^2+4}$

You've identified the x co-ordinate of the points of intersection.
x=4 is unnecessary, as the parabola intersects the rightside part there.

To calculate the area of the bounded region, you only need the area of the part above the x-axis and multiply by 2.

If you also calculate where the parabola and hyperbola cut the x-axis to the left of the y-axis, then you can integrate under the parabola from x=-8 to -3
and integrate under the hyperbola from x=-3 to x=-2.

That will be one way to calculate the area between the curves.

I can't visualise the object itself however, as your question mentions a square.