Find the volume of the solid obtained by rotating the region bounded by x, equals, minus, 6, plus, y, squaredx=−6+y 2 and x, equals, minus, yx=−y about the line x, equals, minus, 9x=−9. Round to the nearest thousandth.

The problem involves finding the volume of a solid obtained by rotating a region bounded by two functions around a line. The functions are x = -6 + y^2 and x = -y. The line of rotation is x = -9.

Here are the steps to solve the problem:

Step 1: Sketch the region bounded by the functions.

Step 2: Identify the outer and inner radius. The outer radius (R) is the distance from the line of rotation to the farthest function, and the inner radius (r) is the distance from the line of rotation to the nearest function.

Step 3: Set up the integral for the volume of the solid using the formula for the volume of a solid of revolution: V = π ∫ [R^2 - r^2] dx.

Step 4: Evaluate the integral.

Step 5: Round the result to the nearest thousandth.

Note: The actual calculations for this problem are quite complex and require knowledge of calculus.