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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