The double cone is a cone on top of another cone. The bottom cone has the circular base on the bottom and the tip on top. The upper cone is upside down, and the two tips touch. Since the vertical plane goes through the tips of both cones, the cross section must have a shape that gets to a point at the middle of the height.
Answer: B. One triangle with the tip on top and an inverted triangle above it with the tips touching.
The two curves intersect at two points, (0, 0) and (8, 8):
The area of a semicircle with diameter is . The diameter of each cross-section is determined by the vertical distance between the two curves for any given value of between 0 and 8. Over this interval, and , so the volume of this solid is given by the integral