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Find the volume of the solid enclosed by the paraboloids x = y² + z² and x = 4 - y² - z²?

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Final answer:

To find the volume of the solid enclosed by the paraboloids x = y² + z² and x = 4 - y² - z², we need to find the intersection points and the enclosed shape.

Step-by-step explanation:

To find the volume of the solid enclosed by the paraboloids x = y² + z² and x = 4 - y² - z², we can first find the intersection points of the two paraboloids. Setting the equations equal to each other, we have y² + z² = 4 - y² - z². Simplifying, we get 2y² + 2z² = 4. Dividing both sides by 2 gives us y² + z² = 2. This is the equation of a circle with radius sqrt(2) centered at the origin.

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