Talia is packing a moving box. She has a square-framed poster with an area of 9 square feet. The cube-shaped box has a volume of 32 cubic feet. Will the posture lie flat in the box? An area of 9 square feet means the square poster has dimensions nothing ft×nothing ft. If the poster were the side of a​ cube, that cube would have a volume of nothing ft3. The box has a ▼ larger or smaller ​volume, so its sides must be ▼ smaller or larger than the sides of the​ poster, meaning that the poster ▼ would not or would lie flat in the bottom of the box.

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)