Final answer:
The volume of the region specified is a hemisphere with a radius of 1. Using the formula for the volume of a sphere, which is V = (4/3)πr³ and then halving it for a hemisphere, the volume is equal to π cubic units.
Step-by-step explanation:
The question is asking for the volume of the region above the disc defined by the equation (x−1)² +y² =1 and below the cone defined by z= √x² +y². This is a problem that involves understanding how to calculate the volume of solid regions bounded by given surfaces, which can often be solved using integral calculus or by recognizing the shapes of known geometrical figures.
Without further details such as the integration bounds or the method for integration, we might turn to geometrical reasoning. The equation given for the disc suggests a circle with a radius of 1 (since (x-1)² + y² = 1 can be viewed as a circle centered on (1,0) with radius 1 if we consider just the x and y terms). The equation for the cone suggests that the cone's apex is at the origin and that it extends outward equally in all directions in the x-y plane.
However, geometric intuition tells us that the volume above the disc and below the cone would actually form a hemisphere, since the cone equation essentially traces out the sides of a hemisphere with radius 1. The formula for the volume of a sphere is V = (4/3)πr³, and thus for a hemisphere (which is half the volume of a sphere), we divide by 2, yielding V = (2/3)π(1³) = (2/3)π cubic units. Therefore, option b) 2/2π would be the correct volume for the hemisphere, but this is not the standard way to present this number, as 2/2 reduces to 1, making the answer simply π cubic units.