Vector Calculus?

Question

Find the volume of the solid bounded by the paraboloids z = 3x^2 + 3y^2 and z = 4 - x^2 - y^2.

I need helpz!

Answer 1

Find the value of z for which the two solids meet. Set the equations equal.

z = 3x² + 3y² = 4 - x² - y²
4x² + 4y² = 4
x² + y² = 1
________

z = 3x² + 3y² = 3(x² + y²) = 3*1 = 3

The open ends of both paraboloids are capped by the plane
z = 3. Calculate the volume of the two solids separately with this limitation.