A designer sketches the region Q in the first quadrant bounded by the x–axis and the two curves
• y=2x
• y=8−x2
The region Q is revolved about the horizontal line y=−4 to create a decorative bowl.
(a) Using appropriate algebraic or numerical methods, determine to the nearest thousandth the two x–coordinates where y=2x and y=8−x2 intersect.
(b) Write a definite integral (or sum of integrals, if necessary) that represents the exact volume of the bowl. Include the correct limits of integration.
(c) Use a calculator to approximate the volume of the bowl to the nearest cubic unit.