# Paraboloid Volume

Calculus Level 5

$z = \dfrac{x^2}{4} + y^2$

The paraboloid given by the equation above is cut by the plane

$z = \dfrac{1}{4} x + 1.$

Find the volume of the region bounded by the paraboloid and the plane. If the volume can be written as $$V = \left( \dfrac ab\right)^2 \pi$$, where $$a, b$$ are coprime positive integers, enter $$a + b$$ as your answer.

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