Acat scan of a human pancreas shows cross-sections spaced 1 cm apart. the pancreas is 12 cm long and the cross-sectional areas, in square centimeters, are 0, 7.9, 15.3, 18.1, 10.2, 10.7, 9.5, 8.5, 7.8, 5.6, 4.2, 2.7, and 0. use the midpoint rule to estimate the volume of the pancreas.

v= cm^3

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)