Teddy has two pairs of black shoes and three pairs of brown shoes. He also has one pair of brown pants and three pairs of black pants. Teddy has two pairs of red socks, four pairs of brown socks and six pairs of black socks. If Teddy chooses a pair of shoes at random, a pair of pants at random, and a pair of socks at random, what is the probability that he chooses shoes, pants, and socks of the same color?

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)